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.

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 [1], 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, L = r 2j& , constancy and the resulting annulling of the
transverse acceleration, rj&& + 2r&j& = L& / r ≡ 0 ) and 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 the observed trajectories of orbital bodies as well as in the produced solutions, the validity of the related First integral ‘status’ of both of these (otherwise, interdependent) quantities should have long been questioned.

Proposed explanation of the Ball Chain Fountain Phenomenon, based on aether pressure gradient nature of Gravity force and formation of internal chain-structure tension, which propagates up the chain's free-falling part, causing the lifting of the part of the chain, i.e. it being pulled out of the jar.

The very way the contemporary science approaches analysis and modeling of complex systems has largely
been determined by the foundations of the classical, analytic and rational mechanics, classical thermodynamics
along statistical mechanics, as well as the essentially probabilistic methodology of the quantum mechanics in
twofold manner: for one thing, the biochemistry and/or the societal systems inherent phenomena as irreversibility,
emergence and/or self-organization, multi-layerdness, dissipativity (in terms of unaccounted for energy inflow),
etc., having been considered as fully alien to the ‘old science’ domains ranging from atomistic/molecular to
cosmology, and for the other – in essentially re-using i.e. somewhat modifying and extending the existing
methodologies, including intra-layers/scales renormalizations [1].
With the advent of working with and development of complex systems pertinent methodologies of analysis
and modeling the awareness is increasing of the need to look at the parts of systems not as being universal and the
way parts “work together” being specific for each system, but rather the parts working together and interacting be
considered and studied in general, and by doing so to be gaining insight into every kind of systems that exist –
from physics and meteorology, over biochemistry, to societal and mental processes.

Since all the systems can ultimately be reduced down to atoms and the pertinent ‘particles’, and having in
mind that physics in that domain had been strongly influenced by the already some more of four centuries old
Kepler’s and subsequent Newton’s works, enough thorough analysis and scrutinizing [2,3] reveals intrinsic
deficiencies of Newtonian and all other ‘mechanics’ and physics (including the GTR) in general, which can be
traced back to formulation of gravitational, and later electric and magnetic fields, as the so-called (single, to more
specific) potential fields, that is fields in which work over closed path (i.e. over the orbital body/particle trajectory)
is zero. Furthermore, due to essentially non-oscillatory form of the pertinent differential equations of motion, to
arrive at the pragmatically satisfying trajectory solutions the two so-called First Integrals (first-order non-linear
differential equations) – time-independent (conserved) total (sum of kinetic and potential) energy and the angular
momentum - have essentially been postulated, based on which – along the indispensable initial conditions (to come
to be considered as the “part of natural laws”) produce solutions which do not satisfy those very “Integrals” !?
Introduction of another, explicitly centrifugal central force/acceleration term proportional to 1/r^3 (besides the
1/r^2 proportional centripetal one) – in line with Kepler’s own physical considerations, over Leibniz’s differentialgeometric
founded proposition, to recent extension and reformulation of the Gordić’s differential set-up - reference
4. in [2]), the non-linear differential equation is produced, the solution of which reveals the non-recursive i.e.
‘chaotic’ behavior, along the possibly inherent multiscaledness & bifurcations. Based on full support of
universality of such modeling that comes from the consistently developed and very compelling Aetherodynamics
(reference 7. in [2]), by the presentation to be prepared will be covered the complex systems relevant topics, as:
Non-conservativeness vs. Conservativeness; Morphysm/Negentropysm vs. Enthropysm; Asymmetry vs.
Symmetry; Multi-scaling vs. Multi-dimensionality, and the Unpredictable Determinism vs. Stochasticity.

[1] Roberts, A.J., Model Emergent Dynamics in Complex Systems, May 25, 2018. (freely downloadable, June ‘18)
[2] Nedic, S., NL-DE based modeling of natural orbital systems without reliance on conservation of energy and
angular momentum, General Science Journal, 2017.
https://www.dropbox.com/s/i756c8w4xbu56sb/Paper_Slobodan_Nedic_NL-DE_GSJ-Submission%20-%20Rev1.pdf?dl=0
[3] Nedic, S., Kepler’s Equation and Angular Momentum.
https://www.dropbox.com/sh/zyaa2bv36yv3shj/AACmw0_lb6nCbYsne3gRiwV1a?dl=0

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 Atsukovsky’s Etherodynamics.

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.

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.

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.

Outgoing from general expectations that the longitudinal electromagnetic waves generating, propagation and reception could support wireless energy transmission and power-efficient wireless communications, 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 Maxwell's equations foundations. 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. Résumé En partant des attentes générales que les ondes électromagnétiques longitudinales pourrait soutenir le transmission de l'énergie et de la puissance-efficace de communication sans fil, le document présent une tentative de surmonter les limites et les contraintes imposés par le cadre des équations classiques de Maxwell. En particulier, elle se concilie les critiques avec le seul promoteur des aspects théoriques et pratiques de la soi-disant technologie des ondes scalaires, en s'appuyant sur quelques-uns des importants résultats de analyse avec le pointage sur des fondations des équations de Maxwell. La motivation est trouvé dans le besoin apparent pour changement de paradigme dans la façon que réseaux sans fil contemporaines sont conçus et exploités, et les attentes contradictoires sur la part de la performance du réseau concernant l'augmentation de débit et de la diminution de la consommation d'énergie visés par la recent lancement et actuel développement et la standardisation de système 5G. La synergie entre de transmission sans fil de l'énergie et de la communication tombe alors dans la ligne avec plus d'un siècle vieux opinions, des convictions et des oeuvres de Tesla.

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...

The very way the contemporary science approaches analysis and modeling of complex systems has largely been determined by the foundations of the classical, analytic and rational mechanics, classical thermodynamics along statistical mechanics, as well as the essentially probabilistic methodology of the quantum mechanics in twofold manner: for one thing, the biochemistry and/or the societal systems inherent phenomena as irreversibility, emergence and/or self-organization, multi-layerdness, dissipativity (in terms of unaccounted for energy inflow), etc., having been considered as fully alien to the ‘old science’ domains ranging from atomistic/molecular to cosmology, and for the other – in essentially re-using i.e. somewhat modifying and extending the existing methodologies, including intra-layers/scales renormalizations [1]. With the advent of working with and development of complex systems pertinent methodologies of analysis and modeling the awareness is increasing of the need to look at the parts of systems not as being universal and the way parts “work together” being specific for each system, but rather the parts working together and interacting be considered and studied in general, and by doing so to be gaining insight into every kind of systems that exist – from physics and meteorology, over biochemistry, to societal and mental processes. Since all the systems can ultimately be reduced down to atoms and the pertinent ‘particles’, and having in mind that physics in that domain had been strongly influenced by the already some more of four centuries old Kepler’s and subsequent Newton’s works, enough thorough analysis and scrutinizing [2,3] reveals intrinsic deficiencies of Newtonian and all other ‘mechanics’ and physics (including the GTR) in general, which can be traced back to formulation of gravitational, and later electric and magnetic fields, as the so-called (single, to more specific) potential fields, that is fields in which work over closed path (i.e. over the orbital body/particle trajectory) is zero. Furthermore, due to essentially non-oscillatory form of the pertinent differential equations of motion, to arrive at the pragmatically satisfying trajectory solutions the two so-called First Integrals (first-order non-linear differential equations) – time-independent (conserved) total (sum of kinetic and potential) energy and the angular momentum - have essentially been postulated, based on which – along the indispensable initial conditions (to come to be considered as the “part of natural laws”) produce solutions which do not satisfy those very “Integrals” !? Introduction of another, explicitly centrifugal central force/acceleration term proportional to 1/r^3 (besides the 1/r^2 proportional centripetal one) – in line with Kepler’s own physical considerations, over Leibniz’s differentialgeometric founded proposition, to recent extension and reformulation of the Gordić’s differential set-up - reference 4. in [2]), the non-linear differential equation is produced, the solution of which reveals the non-recursive i.e. ‘chaotic’ behavior, along the possibly inherent multiscaledness & bifurcations. Based on full support of universality of such modeling that comes from the consistently developed and very compelling Aetherodynamics (reference 7. in [2]), by the presentation to be prepared will be covered the complex systems relevant topics, as: Non-conservativeness vs. Conservativeness; Morphysm/Negentropysm vs. Enthropysm; Asymmetry vs. Symmetry; Multi-scaling vs. Multi-dimensionality, and the Unpredictable Determinism vs. Stochasticity. [1] Roberts, A.J., Model Emergent Dynamics in Complex Systems, May 25, 2018. (freely downloadable, June ‘18) [2] Nedic, S., NL-DE based modeling of natural orbital systems without reliance on conservation of energy and angular momentum, General Science Journal, 2017. https://www.dropbox.com/s/i756c8w4xbu56sb/Paper_Slobodan_Nedic_NL-DE_GSJ-Submission%20-%20Rev1.pdf?dl=0 [3] Nedic, S., Kepler’s Equation and Angular Momentum. https://www.dropbox.com/sh/zyaa2bv36yv3shj/AACmw0_lb6nCbYsne3gRiwV1a?dl=0

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.

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.

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.

Different models of two coupled homogeneous DNA chain vibrations are proposed in the literature. By using as the basic approach to the DNA mathematical modelling published by N. Kovaleva, L. Manevich in 2005 and 2007, we consider a linearized model to obtain main chain subsystems of the double DNA helix. Analytical expressions of the circular eigen frequencies for the homogeneous model of the double DNA chain helix are obtained. The corresponding vibration eigen modes and possibilities of the appearance of resonant regimes as well as dynamical absorption under external excitations are considered. Two sets of normal eigen coordinates of the double DNA chain helix for separation of the system into two uncoupled chains are identified. This may correspond to the base pair order in complementary chains of the DNA double helix in a living cell.

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.

U radu se daje jedna celovita sinteza sveukupnih aktivnosti i istrazivackog stvaralastva 􀀀 od
ribolovackog, preko muzicarskog, 'avanturistickog' i knjizevnog, do matematicarskog, fizicarskog i filozofsko-
epistemoloskog - Mihaila Petrovica Alasa, u kontekstu njegove sveobuhvatne potrage za jedinstvenim analoskim
jezgrom naizgled disparatnih prirodnih pojava. Nj􀀀egovo delo posmatrano je kao sacieno od veoma relevantnih
rezultata i plodnih ideja koje bi trebalo da dovedu do ispunjenja njegovog naucnog, kao i opste-filozofskog i civ-
ilizacijskog ideala - unificiranja svih prirodnih i drustvenih pojva i procesa u jedan zajednicki fizikalno-
matematicki okvir, i tako se doprinese konacnom prevazilazenju tradicionalnih i neodrivih razdeoba u nauci.
Dolazi se do toroidalne vrtlozne strukture kao skalno-invarijantne forme, gde se svemir pojavljuje kao jedna ve-
lika reciklaza materije i kretaa (energije), sa mogucnoscu da njene substancijalne dinamicke i matematicko-
fenomenoloske interakcije obezbede potpunu korespondenciju izmedju eterodinamicki-fizikalnog i matematicko-
logicarskog kontinuuma.

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...

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.∗

This paper presents a non-linear per-bin adaptive equalization in orthogonal multi-carrier data transmission system with the Nyquist-type sub-channel spectral shaping. Previously introduced linear equalization is augmented by three decision feedback filters to improve performance in presence of narrow-band interference (NBI), and to enable exploitation of implicit diversity of multipath fading channels. Adaptation properties of per-bin DFE equalization are analyzed by

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 [1], 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 acceleration,  =  ≡ 0 ) and 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 the observed trajectories of orbital bodies as well as in the produced solutions, the validity of the related First integral ‘status’ of both of these (otherwise, interdependent) quantities should have long been questioned.

Proposed explanation of the Ball Chain Fountain Phenomenon, based on aether pressure gradient nature of Gravity force and formation of internal chain-structure tension, which propagates up the chain's free-falling part, causing the lifting of the part of the chain, i.e. it being pulled out of the jar.

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.

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 Simplectic Integration, Simplectic
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.

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.