Related papers: Another Counter-Example to Dirac's Conjecture

We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in…

The prospect of a time-dependent Higgs vacuum expectation value is examined within the standard model of electroweak interactions. It is shown that the classical equation of motion for the Higgs field admits a solution that is a…

After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown,…

As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…

In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…

In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

We analyse general form of theory with the dynamical determinant of metric. We show that due to the presence of general function of determinant that multiplies scalar curvature Hamiltonian constraint is either second class constraint or it…

Counterfactual explanations can be obtained by identifying the smallest change made to a feature vector to qualitatively influence a prediction; for example, from 'loan rejected' to 'awarded' or from 'high risk of cardiovascular disease' to…

We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian,…

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

We generalize the inequality being a counterpart of the several complex variables version of the Suita conjecture. For this aim higher order generalizations of the Bergman kernel are introduced. As a corollary some new partial results on…

The general solutions with free variable to the second-kind Abel equation, a nonlinear ordinary differential equation that has remained unsolved for nearly two centuries, are presented for the first time by using elementary quadrature…

We argue that the conclusion about the invalidity of the Dirac conjecture, made in the paper by Wang, Li, and Wang (Int. J. Theor. Phys. 48 1894, 2009), was based upon a flawed analysis of the proposed counterexamples. In the case of the…

A description of elementary particles should be based on irreducible representations of the Poincar\'e group. In the theory of massive representations of the full Poincar\'e group there are essentially four different cases. One of them…

This work establishes the existence of addition theorems and double-angle formulas for Ck real scalar functions. Moreover, we determine necessary and sufficient conditions for a bivariate function to be an addition formula for a Ck real…

We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation…

We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…

In this work, we prove global existence of solutions for second order differential problems in a general framework. More precisely, we consider second order differential inclusions involving proximal normal cone to a set-valued map. This…

For arbitrarily large initial data in an open set defined by an approximate Majorana condition, global existence and scattering results for solutions to the Dirac equation with Soler-type nonlinearity and the Dirac-Klein-Gordon system in…