Information transmittal, principle of relativity and mass–energy relation

AbstractRelativistic transformations and their application to electrodynamics of a weakly accelerated electron considered in [A. Einstein, Zur Elektrodynamik der bewegter Körper, Annalen der Physik, 17 (1905) 891–921] are further analyzed in their relation to the principle of relativity, the concept of mass, and the mass–energy equation. Alternative consideration in dynamics of weakly accelerated electrons demonstrates that the factors in longitudinal μβ3 and transverse μβ2 masses of an electron with the mass μ at rest naturally appear in observed accelerations as a result of relativistic transformations, without any deviation from the principle of relativity and the second Newton’s law of motion. As concerns the special relativity in accelerated motion, this allows us to retain the concept of mass as scalar characteristic of an accelerated body. It is argued that “the principle of equivalence of the mass and energy of rest” (Einstein) depends on the speed of the information transmitting signal by which the observation (measurement) is made (synchronization of clocks is achieved), so that relativistic equation E=mc2 appears as an image phenomenon which essentially depends on the propagation of light as a measuring signal and on its speed V=c as the critical parameter of Einstein’s relativistic transformations. It is demonstrated that the spherical waves considered by Einstein are distorted in real time, and the fundamental Lorentz invariant is not crisp, but presents a soft interval whose diameter is in the range of 30,000 km for time delays of 0.1 s in transmission of information. The results open new avenues for further research in the theory of relativity and its applications

Retrieval and use of the balance set in multiobjective global optimization

AbstractIt is shown, on examples, how to compute the balance set and the balance number in Vector Optimization Problems (VOPs) of different nature. New developments are presented concerning possible interrelation between the balance set and the balance number, a new notion of the projection of the balance set onto the parameter space, new approaches for solving VOPs with unbounded objective functions, and some approximation techniques in determining the balance set

Stationarity conditions for linear models

AbstractThe problem of building a linear stationary model for a process given by evenly spaced discrete or continuous observations is considered. Criteria are proposed for the existence of such a model governed by a vector difference or differential equation. Various model representations in discrete and continuous forms are studied and numerical methods for their identification are developed. This gives the order and dynamics of a model in the canonical form. To include processes in noisy environment, a moving average of observations is introduced into deterministic identification algorithms. Different integral forms of the moving average of continuous observations are proposed for identification of models governed by a system of linear stationary differential equations. Discussion of some experimental and computational results is presented

N=3 supersymmetric Born-Infeld theory

We construct an off-shell N=3 supersymmetric extension of the abelian D=4 Born-Infeld action starting from the action of supersymmetric Maxwell theory in N=3 harmonic superspace. A crucial new feature of the N=3 super BI action is that its interaction part contains only terms of the order 4k in the N=3 superfield strengths. The correct component bosonic BI action arises as the result of elimination of auxiliary tensor field which is present in the off-shell N=3 vector multiplet in parallel with the gauge field strength. In this new Legendre-type representation, the bosonic BI action is fully specified by a real function of the single variable quartic in the auxiliary tensor field. The generic choice of this function amounts to a wide set of self-dual nonlinear extensions of the Maxwell action. All of them admit an off-shell N=3 supersymmetrization.Comment: 18 pages, latex, no figures, slight changes, acknowledgements adde

Scale Invariant Low-Energy Effective Action in N=3 SYM Theory

Using the harmonic superspace approach we study the problem of low-energy effective action in N=3 SYM theory. The candidate effective action is a scale and \gamma_5-invariant functional in full N=3 superspace built out of N=3 off-shell superfield strengths. This action is constructed as N=3 superfield generalization of F^4/\phi^4 component term which is leading in the low-energy effective action and is simultaneously the first nontrivial term in scale invariant Born-Infeld action. All higher-order terms in the scale invariant Born-Infeld action are also shown to admit an off-shell superfield completion in N=3 harmonic superspace.Comment: 17 pages; v2: typos correcte

Contiguity and Dynamic Programming

Some aspects of the principle of optimality [1, p.83] are considered, and a modification is proposed for the derivation of the main functional equations of dynamic programming to demonstrate that those equations are valid also in the case of non-optimal remaining trajectories under certain contiguity condition that is defined and analyzed in the paper. Control systems with incomplete information or structural limitations on controls do not, in general, satisfy the contiguity condition. Control problems for such systems may have optimal solutions which, however, cannot be obtained by dynamic programming. This fact is shown on example of a widely used engineering system for which optimal trajectories have all its remaining parts non optimal and non contiguous to the optimal trajectories. The paper presents theoretical justification of dynamic programming for contiguous systems without the principle of optimality, and discussion of some problems important for applications.Рассмотрены некоторые аспекты принципа оптимальности [1, с. 83] и предложена его модификация для вывода основных функциональных уравнений динамического программирования, чтобы показать, что эти уравнения справедливы также в случае неоптимальных остаточных траекторий при некотором условии смежности. Приведены определение и анализ этого условия. Системы управления с неполной информацией или структурными ограничениями управления не удовлетворяют условию смежности в общем случае. Задачи управления для таких систем могут иметь оптимальные решения, но их нельзя получить методом динамического программирования. Этот факт продемонстрирован на примере широко применяемой технической системы, для которой все остаточные части оптимальных траекторий не оптимальны и не смежны с оптимальными траекториями. Дано теоретическое обоснование динамического программирования для смежных систем без принципа оптимальности и рассмотрены некоторые важные прикладные задачи.Розглянуто деякі аспекти принципу оптимальності [1, c.83] і запропоновано його модифікацію для виведення основних функціональних рівнянь динамічного програмування, щоб показати, що ці рівняння є справедливими також у випадку неоптимальних залишкових траєкторій за певною умовою суміжності. Наведено визначення та аналіз цієї умови. Системи управління з неповною інформацією або структурними обмеженнями управління не задовольняють умові суміжності у загальному випадку. Задачі управління для таких систем можуть мати оптимальні розв’язки, але їх не можна отримати методом динамічного програмування. Цей факт показано на прикладі технічної системи, що широко використовується, для якої всі залишкові частини оптимальних траєкторій не оптимальні та не суміжні з оптимальними траєкторіями. Дано теоретичне обґрунтування динамічного програмування для суміжних систем без принципу оптимальності та розглянуто деякі важливі прикладні задачі

Complete Low-Energy Effective action in N=4 SYM: a Direct N=2 Supergraph Calculation

Using the covariant N=2 harmonic supergraph techniques we calculate the one-loop low-energy effective action of N=4 super-Yang-Mills theory in Coulomb branch with gauge group SU(2) spontaneously broken down to U(1). The full dependence of the low-energy effective action on both the hypermultiplet and gauge fields is determined. The direct quantum calculation confirms the correctness of the exact N=4 SYM low-energy effective action derived in hep-th/0111062 on the purely algebraic ground by invoking a hidden N=2 supersymmetry which completes the manifest N=2 one to N=4. Our results provide an exhaustive solution to the problem of finding out the exact completely N=4 supersymmetric low-energy effective action for the theory under consideration.Comment: LaTeX, 21 pages; minor correction

Conformal properties of hypermultiplet actions in six dimensions

We consider scale-invariant interactions of 6D N=1 hypermultiplets with the gauge multiplet. If the canonical dimension of the matter scalar field is assumed to be 1, scale-invariant lagrangians involve higher derivatives in the action. Though scale-invariant, all such lagrangians are not invariant with respect to special conformal transformations and their superpartners. If the scalar canonical dimension is assumed to be 2, conformal invariance holds at the classical, but not at the quantum level.Comment: 14 pages, 1 figur

Complete N=4 Structure of Low-Energy Effective Action in N=4 Super Yang-Mills Theories

Using the ${\cal N}=2$ superfield approach, we construct full ${\cal N}=4$ supersymmetric low-energy effective actions for ${\cal N}=4$ SYM models, with both ${\cal N}=2$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on ${\cal N}=2$ superfield strengths $W$ and ${\bar W}$ to the full on-shell ${\cal N}=4$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form ${ln} W {ln} \bar W$ can be ${\cal N} = 4$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the ${\cal N}=4$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in ${\cal N}=4$ SYM models.Comment: 14 pages, Latex, no figures, slight corrections, refs adde

Renormalizable supersymmetric gauge theory in six dimensions

We construct and discuss a 6D supersymmetric gauge theory involving four derivatives in the action. The theory involves a dimensionless coupling constant and is renormalizable. At the tree level, it enjoys N = (1,0) superconformal symmetry, but the latter is broken by quantum anomaly. Our study should be considered as preparatory for seeking an extended version of this theory which would hopefully preserve conformal symmetry at the full quantum level and be ultraviolet-finite.Comment: 20 pages, 2 figures. An arithmetic error in the calculation of the coefficient of the beta function is corrected. Its sign (corresponding to the Landau zero situation) stays the same as in the earlier version