Slobodan Nedic

After Kepler's formulation of the Three Laws/Rules with the Equation determining the timedependency of the Eccentric and intermediately the True anomalies, and Newton used themalong his first Two Laws and Huygens' circular motion related centrifugal acceleration-to arrive at the with squared distance inversely proportional attracting central force as solely 'governing' the planetary elliptic trajectory orbital motion, the Orbital Mechanics has ever since been modeled by essentially non-oscillatory Non-Linear Differential Equations of the second order. In such situation, in order to solve for the orbital trajectories using initial position and the pertaining velocity, it was indispensable to resort to formulation of two independent 1 st order NL-DEs-one per the degree of freedom: constancy of the sum of kinetic and potential energies-on one side, and the constancy of the angular momentum taken as by the radius swept area velocity, the latter thus implying zero-valued transverse acceleration, both as intrinsically central force features. Subsequently, through developments of Analytic and Rational Mechanics, the general principle of conservativeness was established, characterized by the zero-work done over a closed loop in a potential field-somewhat as the Perpetuity of the 3 rd kind. While for the non-potential forces and situations with presence of dissipative forces the ensuing, notably Hamiltonian formalism has been duly modified, for the natural processes in chemistry and biology in particular, as well in cosmology, the presence of structuring and 'negentropyc' ("negative friction" and/or 'precipitative', the energy inflow) phenomena largely have remained intractable. On the other hand, in the course of his four-years of tedious work on determining the Mars' trajectory [1], guided by his own principle that every motion has its geometrical representation while the latter has to be 'supported' by the truly physical processes, Kepler has very early-at the very stage of the eccentric trajectory hypothesis-realized the necessity of presence of the mechanisms of both the attraction and repulsion, through his "Physical Astronomy", rooted on Gilbert's book De Magnete, assigning to the Sun's virtus-motrics causation of purely circular motion and to a Planet-vis-insitia, the intrinsic ability to modify the very circular motion, [2]. Although this has been largely unaccounted for in the subsequent development of mechanics and dynamics, it had been followed by Leibniz with his by distance's inverse cube explicit centrifugal force, Boscovich's intermittent attraction-repulsion Curve, (Kepler-)Ermakov's Equation, and by this author's extension of the Thermo-Dynamical Oscillator concept of professor Vujo Gordić. These were the reasons for revisiting and scrutinizing the two foundational pillars of the Orbital Mechanics, in particular that it has strongly influenced all the branches of science: physics and cosmology, thermodynamics, non-linear complex systems dynamics, including mathematics.

Milankvić u prvom kratkom članku iz 1912. objašnjava MME na osnovu (Newton-)Ritz-ve emisione teorije, a u drugom iz 1924. - na 50 stranica pokazuje da ni emisiona ni ondulacijona (odnosno, 2. Ajnstajnov postulat) ne mogu da objasne rezultate posmatrnja binarnih-zvezda (usklađivanje dinamike luminoznosti u pomeranja spektralnih linija), i sagledavajući/uvodeći potrebu da se brzina svetrlosti menja u procesu samog prostiranja - predlaže određenu kombinaciju sferičnog i ravanskog talasa, a zapravo bi sva prilika pravo rešenje bilo postojanje re-emisije u zonama inter-stelarnog gasa (mehanizma uvedenog od strane Lenard-a još 1912, kasnije od Kenwood-a? i Oseen-a, pa onda Dowdye-a, Fox-a), a što se jednostavno proverava i u laboratorijskim uslovima ...

Starting from general expectations that the generation, propagation and reception of longitudinal electromagnetic waves in vacuum could provide basis for wireless energy transmission and efficient wireless communication, this paper contributes to overcoming limitations and constraints of the classical Maxwell’s equations framework. That is achieved by confronting the criticism of at least one currently available theoretical scalar waves formulations with a few of the important work results related to scrutinizing of the very foundations of Maxwell’s equations. Also indicated is the ability of the formulation of such phenomena in their present form. By overcoming the traditional constraints and long-held views/convictions regarding nonavailability of longitudinal, that is scalar mechanism generated and propagated in the vacuum, theoretical framework can be created for synergetic approach between wireless energy and information transmission in line with Tesla’s more than a century old...

After 410 years of the formulation and publication (in Astronomia Nova, 1609) of the Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativity, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the fictive one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), incomplete congruence among his physical considerations and the ultimately formulated laws, as well as the paradoxality reflected in the lack of fulfillment of the first Energy integral, and also of the non-existent transverse acceleration implied by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General Aetherodynamics” of V.A. Atukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, P, Savić and V. Vujičić, along the concept of Grand recycling.

After 410 years of the formulation and publication (in Astronomia Nova, 1609) of the Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativity, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the fictive one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), incomplete congruence among his physical considerations and the ultimately formulated laws, as well as the paradoxality reflected in the lack of fulfillment of the first Energy integral, and also of the non-existent transverse acceleration implied by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General Aetherodynamics” of V.A. Atukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, P, Savić and V. Vujičić, along the concept of Grand recycling.

counteracts the effect of shadowing from Le Sage’s surrounding isotropic energy. Both components are as-sumed to be in a dynamical equilibrium, acting in opposite directions along the line connecting a planet and the Sun, having the same ratio as their respective components along the tangent of the planet’s orbit. As result, the only parameters involved are the gravitational constant, which is not necessarily the same as Newton’s, and the planets thermal coefficients, without any reliance on the masses of the two bodies. The planet’s actual trajectory is expected to come out ‘naturally’ from the application of a directly formulated closed path zero-work/minimal-action expression. Applying this principle to explain large-scale phenomena (Andromeda’s dwarf-stars trajectories, and possibly ‘anomalous’ stars velocities, Pioneer 10/11 anomaly, etc.), and its extending it to the atomic level appears quite straightforward, and may furnish fundamental breakthroughs.

counteracts the effect of shadowing from Le Sage’s surrounding isotropic energy. Both components are as-sumed to be in a dynamical equilibrium, acting in opposite directions along the line connecting a planet and the Sun, having the same ratio as their respective components along the tangent of the planet’s orbit. As result, the only parameters involved are the gravitational constant, which is not necessarily the same as Newton’s, and the planets thermal coefficients, without any reliance on the masses of the two bodies. The planet’s actual trajectory is expected to come out ‘naturally’ from the application of a directly formulated closed path zero-work/minimal-action expression. Applying this principle to explain large-scale phenomena (Andromeda’s dwarf-stars trajectories, and possibly ‘anomalous’ stars velocities, Pioneer 10/11 anomaly, etc.), and its extending it to the atomic level appears quite straightforward, and may furnish fundamental breakthroughs.

After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second ("Area") law, the subsequently -- in course of development of Orbital Mechanics -- to the 2${}^{nd}$ law related and formally derived non-existent (zero-valued) transverse acceleration is refuted. Certain implications to Elliptic Integration, Symplectic Integration, Symplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics/dynamics (with the augmented central and torquing forces) are also briefly hinted to.

After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second ("Area") law, the subsequently -- in course of development of Orbital Mechanics -- to the 2${}^{nd}$ law related and formally derived non-existent (zero-valued) transverse acceleration is refuted. Certain implications to Elliptic Integration, Symplectic Integration, Symplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics/dynamics (with the augmented central and torquing forces) are also briefly hinted to.

ABSTRACT This paper presents methods for per-subchannel equalization and echo cancellation in OQAM-based parallel data transmission, which exploit the inherent T/2 AM signaling structure of the orthogonally frequency-division multiplexed T/2-offset quadrature subchannel signals. The method of equalization represents an alternative approach a previously known one, whereas the method of echo cancellation is potentially the only valid solution of this problem for the time being. The computationally efficient realization of echo cancellation is based on the conventional combination of poly-phase (PP) filtering and discrete Fourier transforms in realizing the filter banks. The LMS algorithm convergence behavior is analysed by computer simulation, along with those of a two-step strategy to speed-up the adaptation of the corresponding FIR adaptive structures

ABSTRACT This paper proposes 2x2 MIMO OQAM/FBMC receiver strategy based on successive interference cancellation (SIC) as an extension of the SISO approach which uses entirely real-valued formulation of the transmission system model]. Both increase of throughput and SNR gain are observed through appropriate maximum ratio combining (MRC) of the soft symbols pertaining to the receiver-end diversity branches. The 2x1 multi-user detection (MUD) case has been also addressed to certain extent. Additional gains, essentially related to SISO case, coming from the cooperative use of in-phase (I) and quadrature (Q) branches, primarily based on the quadrature noise components’ independence, as well as from the explicit noise cancellation within the SIC framework, have also been outlined.

Starting from the well-known uniform filter bank multicarrier (FBMC) format with Nyquist spectral shaping of frequency-limited orthogonal (FLO) subchannels and its dual time-frequency, time-limited orthogonal (TLO) form, we introduce an orthogonal frequency division multiplex of nonuniformly spaced subchannels with unequal width. The orthogonality conditions for nonuniform FBMC (Nu-FBMC) were evaluated through simulations using the ‘extended orthogonal frequency division multiplexing (OFDM)’ framework, as well as through analytical derivation in a rather pragmatic manner. The referent filter bank impulse responses were defined in frequency domain by straightforward aggregations of the pertaining uniform filter bank subchannels spectral shapes for FLO and by transforming the frequency domain of appropriately aggregated time-limited referent impulse responses of uniform TLO configuration. Nonsymmetrical spectral shaping of subchannels in the FLO case format has also been proposed. The...

In this submission it will be shown that the consequent application of the concept of “vector at the point” of [2] essentially represents the missing link, and that the covariant differentiation/integration essentially reduces to the simple rotationally-invariant transformation between the two coordinates systems, the related rotation matrix essentially ‘absorbing’ the location/time variant components of the (normalized) basis vectors, thus avoiding the problematic geometrizing of essentially algebraic realm. Along the illustration of the consistency of the absolute differentiation/integration without the necessity to us the Christoffel symbols in the context of orbital mechanics and the Newton-Keplerian elliptic trajectories  [5], it will be mentioned the resolution of the generalized integration of the Euler’s spinning top equation [6], and some critical remarks on covariant differentiation given.

This paper addresses aspects of power and spectral efficiency advantages of OFDM/OQAM over the conventional OFDM (with QAM) signaling and accessing format for wireless networks and cognitive radio (CR) applications. The emphasis is on the ability of the OFDM/OQAM format to work without cyclic-prefix (CP), and to have a relatively small number of subchannels without incurrence of power and spectral losses inherent to OFDM/QAM heavy reliance on it. Specifically, the following aspects are elucidated: 1) exponentially increasing Eb/No degradation in OFDM with increasing QAM constellations size, and 2) reduced PAPR in OFDM/OQAM and consequently better PSD mask fitting. These two aspects are supported by computer simulation results. Additional OFDM/OQAM advantages, as the multipath diversity gains, are also briefly discussed.

The Newtonian mechanic and contemporary physics model the non-circular orbital systems on all scales as essentially conservative, closed-path zero-work systems and circumvent the obvious contradictions (rotor-free ‘field’ of ‘force’, in spite of its inverse proportionality to squared time-varying distance) by exploiting both energy and momentum conservation, along specific initial conditions, to be arriving at technically more or less satisfactory solutions, but leaving many of unexplained puzzles. In sharp difference to it, in recently developed thermo-gravitational oscillator approach movement of a body in planetary orbital systems is modeled in such a way that it results as consequence of two counteracting mechanisms represented by respective central forces, that is gravitational and anti-gravitational accelerations, in that the actual orbital trajectory comes out through direct application of the Least Action Principle taken as minimization of work (to be) done or, equivalently,...

Outgoing from the known uniform FBMC (Filter-Bank Multi-Carrier) formats with Nyquist spectral shaped sub-channels and its time-frequency dual Time-Limited Orthogonal (TLO) form, we introduce an orthogonal frequency division multiplex of nonuniformly spaced and unequal-width sub-channels. The goal is to attain potential gains in using relatively small number of subchannels, but still allow for frequency gaps needed for channelization with a small decrease in overall spectral efficiency. The orthogonality conditions are evaluated through simulations using the extended OFDM framework, whereby the corresponding referent filter-bank impulse responses are defined in frequency-domain by straightforward aggregations of the pertaining uniform filter-bank sub-channels spectral shapes (for conventional FBMC with frequency limited sub-channels spectra), and by transforming to frequency-domain of adequately aggregated time-limited referent impulse responses of uniform TLO configuration. An anal...

This White Paper summarizes results of waveform oriented studies under the FP7-ICT project EMPhAtiC. The focus is on filter bank based multicarrier and single carrier waveforms with highly enhanced spectrum containment compared to OFDM or OFDM-based SC-FDMA. This feature is crucial for the targeted heterogeneous coexistence scenario of the novel Broadband Professional Mobile Radio (B-PMR) system with legacy narrowband systems of the TETRA family operating in the same frequency band. The reported investigations cover (i) filter bank design and structures, with emphasis on increased flexibility and multimode capability, (ii) channel estimation, equalization and synchronization, (iii) effects of nonlinear transmitter high power amplifier, (iv) spectrum sensing functionality needed in adhoc operation of B-PMR devices, and (v) demonstration of the developed techniques and overall solution with real hardware.

A new receiver structure for improving the performance of conventional discrete multitone (DMT) based digital subscriber line (DSL) transceivers is described. In this method, the conventional demodulator consisting of a FFT followed by a scalar frequency-domain equalizer is augmented by an additional data-path utilizing windowing. Time-limited receiver windowing is done independently for each symbol over the orthogonality interval while the transmitter is unchanged. Windowing can be carried out efficiently in the time or frequency domain. A decision feedback equalizer is used to cancel the resulting inter-bin-interference. Computer simulation results are presented for ADSL with realistic interference conditions which show that this method is most effective against narrowband interference and other impairments which lead to diminished inter-bin orthogonality. The overall technique is also applicable to other multi-carrier modems such as VDSL and wireless OFDM.

Based on the list of research topics that Milanković had conceived for the Mathematical and Astronomical institutes (one plus two), as well as for the aspirants’ and doctoral theses (eight plus fifteen) – as found out by mathematician and science-historian Dragan Trifunović back in 1978, in this article is made an attempt to establish the reasons of those which relate to the need of re-examining and further developing the very theory of gravity and the traditional formulation of the natural orbital motion, having in mind that – through the secular changes of eccentricities and other parameters of planetary trajectories – they are in direct connection with the methodology and results of his “Solar Cannon”. In the anticipation of the geologically and otherwise experimentally estblished need for the fundamental modification of the Newtonian orbital mechanics/dynamics, it is brought-up and reaffirmed – starting from as early as the Kepler’s physical considerations - the Leibniz’s two-components central acceleration, which is shown to be arrivable at by using the Milanković’s distance inverse squared dependence of planets’ temperatures within the context of Gordić’s differential formulation of orbital motion as dynamic equilibrium between the gravitational (attractive) and thermal (repulsive) components of central ‘force’. It is hinted to the important correspondence with the somewhat more than one and the half century old formulation through the Kepler-Ermakov non-linear differential equation and the relevance of its application in the context of the “archeological astronomy” and asteroids dynamics modeling, as well as on the astrophysical, astronomic and cosmogony plans, through essentially obsoleting the “dark matter” and “dark energy” problems/issues. The additional support for adequacy of the formulation of the planetary orbital motion as the Thermo-Gravitational Oscillator has been found in the foundation and implications of the Atshukovsky’s Etherodynamics.

After 410 years of the formulation and publication (in Astronomia Nova, 1609) of the Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativity, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the fictive one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), incomplete congruence among his physical considerations and the ultimately formulated laws, as well as the paradoxality reflected in the lack of fulfillment of the first Energy integral, and also of the non-existent transverse acceleration implied by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General Aetherodynamics” of V.A. Atukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, P, Savić and V. Vujičić, along the concept of Grand recycling.

The Newtonian mechanic and contemporary physics model the non-circular orbital systems on all scales as essentially conservative, closed-path zero-work systems and circumvent the obvious contradictions (rotor-free 'field' of 'force', in spite of its inverse proportionality to squared time-varying distance) by exploiting both energy and momentum conservation, along specific initial conditions, to be arriving at technically more or less satisfactory solutions, but leaving many of unexplained puzzles. In sharp difference to it, in recently developed thermo-gravitational oscillator approach movement of a body in planetary orbital systems is modeled in such a way that it results as consequence of two counteracting mechanisms represented by respective central forces, that is gravitational and anti-gravitational accelerations, in that the actual orbital trajectory comes out through direct application of the Least Action Principle taken as minimization of work (to be) done or, equivalently, a closed-path integral of increments (or time-rate of change) of kinetic energy. Based on the insights gained, a critique of the conventional methodology and practices reveals shortcomings that can be the cause of the numerous difficulties the modern physics has been facing: anomalies (as gravitational and Pioneer 10/11), three or more bodies problem, postulations in modern cosmology of dark matter and dark energy, the quite problematic foundation of quantum mechanics, etc. Furthermore, for their overcoming, indispensability of the Aether as an energy-substrate for all physical phenomena is gaining a very strong support, and based on recent developments in Aetherodynamics the Descartes' Vortex Physics may become largely reaffirmed in the near future.

Starting from Le Sage’s theory of gravitation, we postulate that the thermal energy of a planet essentially counteracts the effect of shadowing from Le Sage’s surrounding isotropic energy.  Both components are assumed to be in a dynamical equilibrium, acting in opposite directions along the line connecting a planet and the Sun, having the same ratio as their respective components along the tangent of the planet’s orbit.  As result, the only parameters involved are the gravitational constant, which is not necessarily the same as Newton’s, and the planets thermal coefficients, without any reliance on the masses of the two bodies.  The planet’s actual trajectory is expected to come out ‘naturally’ from the application of a directly formulated closed path zero-work/minimal-action expression.  Applying this principle to explain large-scale phenomena (Andromeda’s dwarf-stars trajectories, and possibly ‘anomalous’ stars velocities, Pioneer 10/11 anomaly, etc.), and its extending it to the atomic level appears quite straightforward, and may furnish fundamental breakthroughs.

Outgoing from the known uniform FBMC (Filter-Bank Multi-Carrier) formats with Nyquist spectral shaped sub-channels and its time-frequency dual Time-Limited Orthogonal (TLO) form, we introduce an orthogonal frequency division multiplex of non-uniformly spaced and unequal-width sub-channels. The goal is to attain potential gains in using relatively small number of sub-channels, but still allow for frequency gaps needed for channelization with a small decrease in overall spectral efficiency. The orthogonality conditions are evaluated through simulations using the extended OFDM framework, whereby the corresponding referent filter-bank impulse responses are defined in frequency-domain by straightforward aggregations of the pertaining uniform filter-bank sub-channels spectral shapes (for conventional FBMC with frequency limited sub-channels spectra), and by transforming to frequency-domain of adequately aggregated time-limited referent impulse responses of uniform TLO configuration. An an...

An attempt to provide derivation of the velocity of a hypothetical electromagnetic perturbation in the form of a Dirac-Delta function is made by using the Galilean space-time transformation for its individual frequency components. It has been indicated that the related light propagation speed is independent of the velocity of the emitting body. On the other hand, if the relativistic (Lorenz) transformations are used, an ambiguous solution is produced. This might serve as an indirect proof for validity of the classical transformation of space and time, since conceptually it is satisfying that if velocity of any form of perturbation could be invariant, then it should be the one that lasts over so short a time interval that the sources’ velocity cannot be imparted to it.

This paper addresses aspects of power and spectral efficiency advantages of OFDM/OQAM over the conventional OFDM (with QAM) signaling and accessing format for wireless networks and cognitive radio (CR) applications. The emphasis is on the ability of the OFDM/OQAM format to work without cyclic-prefix (CP), and to have a relatively small number of subchannels without incurrence of power and spectral losses inherent to OFDM/QAM heavy reliance on it. Specifically, the following aspects are elucidated: 1) exponentially increasing Eb/No degradation in OFDM with increasing QAM constellations size, and 2) reduced PAPR in OFDM/OQAM and consequently better PSD mask fitting. These two aspects are supported by computer simulation results. Additional OFDM/OQAM advantages, as the multipath diversity gains, are also briefly discussed.

DESCRIPTION We have found that the so-called anomalous acceleration of the Pioneer 10 and 11 spacecrafts results from inadequate estimation of the signal round trip propagation time, so that, based on the radar ranging equation, the measured Doppler shift depends not only on relative velocity, υ, but also depends on actual acceleration, ‘jerk’, etc. The inadequacy of the propagation time pertains to difference between the Round Trip Light Time (RTLT) based on the invariant constant c and its modification by the factor 1+2 υ/c. Numerical results produced with some simplifications from the available Pioneer 10 and 11 ephemeris data very well match the established difference between the Doppler inferred observational and modeled spacecraft velocities both in direction and the amount of the reported anomalous acceleration. Implications and connections to the solar pressure modeling, other spacecrafts’ observations, other’s explanations and relevance to cosmological red-shift are briefly...

counteracts the effect of shadowing from Le Sage’s surrounding isotropic energy.  Both components are as-sumed to be in a dynamical equilibrium, acting in opposite directions along the line connecting a planet and the Sun, having the same ratio as their respective components along the tangent of the planet’s orbit.  As result, the only parameters involved are the gravitational constant, which is not necessarily the same as Newton’s, and the planets thermal coefficients, without any reliance on the masses of the two bodies.  The planet’s actual trajectory is expected to come out ‘naturally’ from the application of a directly formulated closed path zero-work/minimal-action expression.  Applying this principle to explain large-scale phenomena (Andromeda’s dwarf-stars trajectories, and possibly ‘anomalous’ stars velocities, Pioneer 10/11 anomaly, etc.), and its extending it to the atomic level appears quite straightforward, and may furnish fundamental breakthroughs.

Outgoing from the overwhelming evidence for untenability of the Einstein’s Second postulate on light speed invariance for two inertial systems moving with respect to each other, firstly a crucial Reductio-ad-Absurdum proof has been provided, followed by the proposal for experimental verification for the mechanism of increasing or decreasing the group light signal velocity by relative motion of transmitter with respect to the receiver. The proposed experiment emulates the binary stars configuration, without any intervening interstellar medium, that - based on up-to-date Ritz’s Emission Theory – ‘amortizes’ the light velocity during the propagation and contributes to discrepancy between the variations in stars’ luminosity and the Doppler shifts presented in line spectra as received on Earth.
Experimental results of the proposed set-up can be used as Proof of Concept for feasibility of both imposing delay and advancement of optical signals, so that by heavy downsizing of the propoed experimental set-up through utilization of nano-technology and related photonics advancements, the time of arrival of optical signals can be appropriately adjusted (with accompanying signals time-frequency domain scaling) to enable implementation of entirely optical multiplexers, routers and synchronizers. To provide comparison with the conventionally pursued methods which emulate the electronics-based digital signals processing technology, bit- and packet-level multiplexers are used.

As contribution to Tesla’s insights and convictions regarding the inner working principles of the “Wheel of Nature” and concept of Ether as an energy substance from which everything comes into being and to what it returns, the mechanism intrinsic to the natural (primarily macro-scale) orbital systems is revealed. Starting from the Le Sage-an theory of gravitation as the virtually attracting mechanism of ‘being-pushed’ instead of ‘being-pulled’, the global thermal energy of a planet essentially is counteracting (through its structural change or directly opposing) the mutual (bodies’-Sun) shadowing from the surrounding homogeneous and isotropic “space energy”, that is the Ether. The two essentially thermal components are taken to be in dynamical equilibrium, by acting in opposite directions along the line connecting a planet and the Sun. As result, the only parameters involved are the gravitational constant (which Tesla thought should be different for different bodies within a constellation) and the planets’ specific temperature coefficient, without any Newtonian or GTR-vistic reliance on masses of the bodies.
The planets’ actual trajectories are expected to result naturally from the application of the Principle of Least action, resulting in dynamically stable non-conservative systems, whereby the bulk of the resulting energy is supplied from the Ether, contrary to the Newtonian and generally physics’ notion of orbital systems on all scales as essentially conservative, zero-work  systems. By straightforwardly applying this principle to explain large-scale cosmological phenomena, various paradoxes, as well as the still not satisfactorily resolved Pioneer 10/11, and extending it to the nan-scale Casimir effect related over-unity system build-up attempts, fundamental breakthroughs are likely to result. In all this, the foundation of modern physics is debunked through still not fully refuted Aristotle’s assertion on higher velocity of heavier falling bodies (reflected in the central role of the mass) and his still unappreciated “Unmoved Mover” concept.

Outgoing from the well known synchronous serial data transmission system of Nyquist or partial response type, and actual dual system is introduced in this paper according to the principles established by Bello. Polyphase networks with DFT processing are used to extend time-frequency duality relationship existing between serial and standard parallel data transmission systems. Benefits gained from viewing a standard parallel system as dual of serial one are discussed in a rather qualitative manner. Some quantitative results are provided with respect to combating the effects of multiplicative noise, based on automatic adaptive equallization in transformed domain.

Cyclic spectral analysis of OFDM/OQAM signals with cyclostationary signature is performed by the proposed matrix-based stochastic method based on their Markov chain representation. An exact expression for the cyclic spectrum of these signals is derived, and the corresponding cyclic features are analyzed.

Starting from strictly distinguishing between the 'transformation' of the coordinates of a point defined by their functional relation itself and the transformation of the coordinates of a vector / tensor (velocity, acceleration, gradient, displacement)-at the point (in line with the Vujičiċ's coordinates-independent point's position vector formulation), by applying the unified procedure of forming the corresponding basis vectors, derivation of the covariantly consistent components of the acceleration in the trajectories' coordinates base is accomplished, which turn out formally (presence of the second instead of the third derivatives of coordinates) and substantively (tractability of non-autonomous non-linear differential equations modeling) to be different from traditionally used heuristically/ad-hoc formulated "natural" tangent-normal coordinates. As a very important and far-reaching implication, by relying on numerical integration for the case of Orbital Motion, illustrated is the importance and effectiveness of a consistent (rotational-invariant) approach as an indicator of possible essential (in)correctness of the formed dynamic models, as well as the need for separation of kinematics and dynamics related parts of non-linear differential equations. Also, a kind of tensor's 'vectorization' is suggested to be thought of as the means to check for the validity of various tensors calculus formalisms, including the spatial derivatives. .

In this paper is given a holistic synthesis of the overall activities-from fishing, over musical, 'adventurist' and literal, to mathematical, physical and philosophic-epistemologicalof Michael (Mihailo) Petrović Alas, in the context of his all-encompassing search for the unique analogue core of all the seemingly disparate phenomena. His work is viewed at as consisted of very relevant results and fruitful ideas which should contribute to fulfillment of his scientific, as well as overall-philosophic and civilizational ideal-the unification of all natural and social phenomena and processes into one common physical-mathematical framework, and thus contributing to the ultimate overcoming of the traditional and untenable "compartmentalization" of the science. It is arrived at the toroidal vortex structure as the scale-invariant form, whereby the universe appears as a grand recycling of matter and movement (energy), with opening the perspective for modeling its substantial dynamical and mathematical-phenomenological interactions to approach the full correspondence between the aetherodynamics-physical and the mathematics-logical continuum.

Спустя 412 лет от сформулировки и публикации (в Astronomia Nova) уравнения Кеплера, которое связывает эксцентрическую (и, посредова-телъно, истинную) аномалию траекторий планет с равномерно текущим временем, в соответствии с его Вторым законом площадей, впоследствии-в процессе развития орбитальной механики-с вторим законом Кепле-ра связанное и формально выведенно как несуществующее (нулевое) по-перечное ускорение- пересматривается. Кратко указуегся на некоторые по-следствия для эллиптической интеграции, симплектической интеграции, симплектической геометрии/топологии, а также на связь между физи-ческими и математическими континуумами в контексте многоуровневой масштабно-инвариантной механики/динамики, с прибавленными истинно центробежной к притягивающей и соответствующей крутящией сылами. Ключевые слова: Уравнение Кеплера, Закон площадей, Первые интегра-лы, Орбитальная механика, Неконсервативность. Введение Помимо полной энергии, состоящей из суммы кинетической и потен-циальной энергий, это также момент количества движения (L = r 2φ) ор-битального тела, который считается неизменным в течении орбитально-го периода (T), таким образом формируя так называемые (два) Первые интегралы для процесса решения с ними связанных (по сути, не коле-бательных) нелинейных дифференциальных уравнений движения. Хотя относительно легко показать, что интеграл энергии является неоснова-тельным, то есть противоречивым постулатом 1-либо путем прямой аналитической и численной оценки и/или формально применяя полную производную по времени от соответствующего дифференциального выра-жения (Приложение A в расширенной версии статьи, со ссылкой в сноске 4), для углового момента-и его аналога в форме второго закона Кеплера-это становится очень субтильной и достаточно сложной задачей. Одна-ко, вследствие самого присутствиа ненулевого тангенциального ускорения 1 Довольно редкие авторы учебников пытаются доказать его достоверность либо через предполагаемую коллинеарность векторов положения и скорости-по существу невыполненных либо в начальных условиях либо в полученных решениях, или полагаясь на полностью нулевое значение-иначе справедливо только на апсидах-поперечного ускорениа, что на самом деле опровергается в этой статье.

After 412 years of the formulation and publication (in Astronomia Nova, 1609) of the
Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativeness, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the
fictitious one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), the incomplete congruence among his physical considerations
and the ultimately formulated laws, and also of the non-existent transverse acceleration ‘implied’ by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General
Aetherodynamics” of V.A. Atsukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, and P, Savić. Certain implications to the Elliptic Integration, the Symplectic Integration, Symplectic Geometry/Topology, as well as the connection between physical and mathematical continua in the context of the multi-level, scale-invariant mechanics and/or dynamics - will be briefly mentioned.

U radu se daje jedna celovita sinteza sveukupnih aktivnosti i istraživačkog stvaralaštva - od ribolovačkog, preko muzičarskog, 'avanturističkog' i književnog, do matematičarskog, fizičarskog i filozofsko-epistemološkog - Mihaila Petrovića Alasa, u kontekstu njegove sveobuhvatne potrage za jedinstvenim analoškim jezgrom naizgled disparatnih prirodnih pojava. Njegovo delo posmatrano je kao saqičeno od veoma relevantnih rezultata i plodnih ideja koje bi trebalo da dovedu do ispunjenja njegovog naučnog, kao i opše-filozofskog i civilizacijskog ideala - unificiranja svih prirodnih i društvenih pojav i procesa u jedan zajednički fizikalno-matematički okvir, i tako se doprinese konačnom prevazilaženju tradicionalnih i neodrživih razdeoba u nauci. Dolazi se do toroidalne vrtložne strukture kao skalno-invarijantne forme, gde se svemir pojavljuje kao jedna velika reciklaža materije i kretanja (energije), sa mogućnošću da njene substancijalne dinamičke i matematičko-fenomenološke interakcije obezbede potpunu korespondenciju između eterodinamički-fizikalnog i matematičko- logičarskog kontinuuma.

Abstract in English: In this paper is given a holistic synthesis of the overall activities 􀀀 from fishing, over musical, ’adventuristic’ and literal, to mathematical, physical and philosophic-epistemological 􀀀 of Mihailo Petrovi Alas, in the context of his all-encompassing search for the unique analogue core of all the seemingly disparate phenomena. His work is viewed at as consisted of very relevant results and fruitful ideas which should contribute to fulfillment of his scientific, as well as overall-philosophic and civilizational ideal 􀀀 the unification of all natural and social phenomena and processes into one common physical-mathematical framework, and thus contributing to the ultimate overcoming of the traditional and untenable "compartmentalization" of the science. It is arrived at the toroidal vortex structure as the scale-invariant form, whereby the universe appears as a grand recycling of matter and movement (energy), with possibility of its substantial dynamical and mathematical-phenomenological interaction to ensure the full correspondence between the aetherodynamics-physical and the mathematics-logical continuum.

После 410 година од фомулисања и објављивања (у Astronomia Nova, 1609) Кеплерове Једначине, која повезује екцентричну (и, посредно, праву) аномалију планетарних путања са униформним током времена, у складу са његовим Другим законом Површине, у раду се сагледавају са тим повезане изгледне недостатности основа орбиталне механике и динамике, проузроковане изостајањем Кеплерових пратећих физикалних промишљања, а које се реперкутују на: ослањање на такозване Инваријанте - Прве интеграле Енергије и Момента Количине Кретања, имплицитну Конзервативност, канонички формализам и свеприсутност Принципа Симетрије, као и суштинско недостајање експлицитне центрифугалне силе и њено надомештање фиктивном. Даје се приказ Кеплерових настојања и постигнутих резултата, као и њгове кључне позиције у историјском развоју механике, физике, астронимије и астрофизике, као и науке уопште - кроз увиде у одграњавање развоја науке преко Њутна (уместо преко Декарта и Лајбница), некомплентну подударност његових физикалних разматрања и коначно формулисаних закона, као и парадоксалности које се огледају у незадовољености како Првог интеграла (енергије), тако и Другим законом имплицираном непостојању трансферзалног убрзања. У прилог исправности запостављеног правца развоја и фундаменталности Кеплерових увида у потребу постојања како привлачних, тако и одбојних интеракциа орбиталних тела и централног тела – Сунца, реафирмише се Кеплер-(Ј)Ермаковљева нелинеарна диференцијална једначина другог реда и њена адекватност за феноменолошко моделирање динамичких интеракција на свим ‘скалама’ природе: уз кратак осврт на “Општу Етеродинамику” В.А. Ацјуковског, као основу за баштињење и оправданост увида/резултата Декарта, Лајбница, Бошковића, Даламбера, Енгелса. Х. Страхеа, М. Петровића, М. Миланковића, П. Савића и В. Вујичића, и концепт Велике рециклаже. Abstract in English: After 410 years of the formulation and publication (in Astronomia Nova, 1609) of the Кеpler’s Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly flowing time, in accordance with his Second (surface) law, in this paper are perceived with it connected certain deficiencies of the orbital mechanics and dynamics, caused by absence of the Kepler’s accompanying physical considerations, and which are repercuted in: reliance on the so-called Invariants – the First integrals of Energy and of the Angular Momentum, implicit Conservativity, canonic formalism and omnipresence of the Symmetry principle, as well as the essential lacking of the explicit centrifugal force and its substitution by the fictive one. It is given а survey of the Kepler’s strivings and the results attained, as well as of his key role in the historical development of the mechanics, physics, astronomy and astrophysics, and the science in general – through insights in the branching of the science development over Newton (instead over Descartes and Leibniz), incomplete congruence among his physical considerations and the ultimately formulated laws, as well as the paradoxality reflected in the lack of fulfillment of the first Energy integral, and also of the non-existent transverse acceleration implied by the Kepler’s Second law. In support of the justification of the neglected development direction and the fundamentality of the Kepler’s insights in the need for both the attractive an repulsive interactions of the orbital and central body – the Sun, the Kepler-Ermakov second order non-linear differential equation has been reaffirmed along its adequacy for the phenomenological modeling of dynamic interactions on all the ‘scales’ in Nature: with brief reference to the “General Aetherodynamics” of V.A. Atukovsky, as the basis for reuse and justification of insights/results of Descartes, Leibniz, Boscovich, D’Alambert, Engels, H. Strache, M. Petrović, M. Milanković, P, Savić and V. Vujičić, along the concept of Grand recycling.

In difference to traditionally established determination of planetary orbits in the " potential force fields " by reliance on the postulated first integrals and with implicit avoidance of direct involvement of the time-parameter t, proposed is the orbital motion modeling based on use of a set Non-Linear Differential Equations of motion with provision of explicit centrifugal ('anti-gravitational') force and the implied torque, allowing for the explicit oscillator-like nature of the underlying system of the Kepler-Ermakov type and use of the related exact integration invariants. The untenability of the Kepler-Newtonian invariants has been supported by both analytical derivations and numerical evaluations. Besides by the numerical integration, the previously formulated Termo-Gravitational Oscillator configuration has been evaluated in its integral form. The positive-valued work pertinent to the (quasi-)closed orbital trajectories opens up prospects of the Least Action Principle application as its direct minimization and the awareness of 'precipitativeness' as energy inflow intrinsic feature of the " open " (thermo-)dynamical systems.

Outgoing from general expectations that the longitudinal electromagnetic waves generating, propagation and reception could support wireless energy transmission and power-efficient wireless communications, in this paper attempts to contribute to overcoming limitations and constraints of the classical Maxwell’s equations framework. In particular, it goes about conciliating the critics and the only proponent of theoretical and practical aspects of the so-called scalar waves technology, by relying on a few of important work results on scrutinizing the very foundations Maxwell’s equations. The motivation is found in the apparent need for the paradigmatic shift in the ways the modern wireless networks radio links, topology and energy supply are designed and operated, and the quite contradictory expectations on part of the network performance regarding the throughput increase and the energy consumption decrease targeted by the recently initiated and currently ongoing development and standardization of 5G system. The synergetic approach between wireless energy transmission and communications then falls in line with Tesla’s more than a century old views, convictions and works.

It has been found that the Kepler’s (un)fortunate and essentially unallowable, but literally “life-rescuing” systematic modification of the Mars’ trajectory measured positions, despite his subsequent explanation that the Area law – valid for the angle(s) time-dependencies determined by his Equation – pertains to the solely Sun-governed circular motion, has led to the combining of circular (through the angular momentum  constancy and the resulting annulling of the transverse accelerationand rectilinear motions (through the constancy of total energy, which is nothing else than the definitional relation of the potential energy as the acquired and/or lost kinetic energy in the potential field)  as orbital motion’s two Prime integrals.  However, since the very presence of non-zero tangential acceleration in theobserved trajectories of orbital bodies as well as in the produced solutions, thevalidity of the related First integral ‘status’ of both of these (otherwise, interdependent) quantities should have long beenquestioned.
The above expression for transverse acceleration and the corresponding one for the total energy are given in the so-called “non-inertial coordinate system”, which has turned out to be rotationally-invariant to the rectangular one, so that the numerical integration in both, as well as the analytic-numerical evaluations, produce the same results corroborating the outgoing integrals. However, when evaluating in the tangential-normal generalized coordinates (numerical integration will be pursued, too) the following is realized:
1. One gets the non-zero tangential acceleration, the projection of which on the transverse direction produces non-zero transverse acceleration;
2. Integrating the gravitational force projection on tangential direction for the vertically scaled nominal ellipse with the pertinent KE, one gets the positive energy-well.

Based on this, as well as the fact that there are numerous situations where the (closed) elliptic trajectories with two central or non-central forces do not obey the area-law and Kepler’s equation, the principle of conservativeness should be reconsidered and possibly be altogether abandoned.

On the other hand, the “Kepler’s Physical Astronomy” based on his own principle that every motion has its geometrical representation while the latter has to be ‘supported’ by the truly physical processes, Kepler has very early – at the very stage of the eccentric trajectory hypothesis – realized the necessity of presence of the mechanisms of both the attraction and repulsion, through his “Physical Astronomy”, rooted on Gilbert’s book De Magnete, assigning to the Sun’s virtus-motrics causation of purely circular motion and to a Planet – vis-insitia, the intrinsic ability to modify the very circular motion. Although this has been largely unaccounted for in the subsequent development of mechanics and dynamics, it had been followed by Leibniz with his by distance’s inverse cube explicit centrifugal force, Boscovich’s intermittent attraction-repulsion Curve, (Kepler-)Ermakov’s Equation, and by this author’s extension of the Thermo-Dynamical Oscillator concept of professor VujoGordić  - all this justifying Kepler’s insights.

Based on insights gained from two Milanković’s papers the subject of which was consideration and scrutinizing of the Second Postulate of the Special Theory of Relativity, and from his “Book of memories and recollections from 1909 to 1944”, in this paper provided are the reasons for his preoccupation with this problematic. Whereas in the article from 1912 he briefly hints the way towards explaining the result of the Michelson-Morly experiment by the (Ritz’s) Emission Theory, in the fifty pages long paper from 1924 he thoroughly analyses the possible dependency of the phase velocity of light and/or electromagnetic perturbation on velocity of the emitting body, and in the context of relationship of changes in the binary-star’s luminosity and Doppler-shifts in spectra of their chemical elements establishes that the Emission Theory cannot satisfy the set-up criteria. Only in the last section of that paper one can suspect the Milanković’s implicit inclination towards the Emission Theory, since therein he provides a short analysis of the possibility that the propagation velocity actually is getting changed during propagation. The newest understanding of somewhat extended emission theory, with the support of the Atsukovsky’s Etherodynamics, based on which the propagation velocity is invariant w.r.t. the transmitter, indeed leads to the re-emission based mechanism of ‘amortization’ of the light propagation velocity with retention of the classical Doppler-shifts. Towards re-affirmation of the Milankoviić’s tacit anti-relativistic position, as well as for establishing the right basis for astronomical observations, as per Milanković’s insights and expectations, in this article will be given two relevant author’s results: absurdity of the Second STR Postulate for the two-dimensional Dirac-delta perturbation, and the proposition for the experiment which emulates the binary-star configuration, without influence of the inter-stellar gases as mediators. In this context will also be referred to the relevant aspects of the GPS system’s operation.