We address the problem of reshaping light in the Schrödinger optics regime from the perspective of optimal control theory. In technological applications, Schrödinger optics is often used to model a slowly-varying amplitude of a para-axially propaga...
We study the Hubbard model on a geometrically-frustrated hyperkagome lattice by a cluster extension of the dynamical mean field theory. We calculate the temperature ($T$) dependences of the specific heat ($C$) and the spin-lattice relaxation time (...
We report equations of motion for the occupation numbers of natural spin orbitals and show that adiabatic extensions of common functionals employed in ground-state reduced-density-matrix-functional theory have the shortcoming of leading always to o...
This paper describes necessary elements for constructing theoretical models of network and system administration. Armed with a theoretical model it becomes possible to determine best practices and optimal strategies in a way which objectively relat...
Stark-Heegner points are conjectural substitutes for Heegner points when the imaginary quadratic field of the theory of complex multiplication is replaced by a real quadratic field $K$. They are constructed analytically as local points on elliptic cu...
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer hold. Nevert...
The relentless efforts of the physics community has not yet availed us the solution of how to unify the Quantum Mechanics with General Relativity, a puzzle that has engaged the minds of the physicists for almost a century. The insufficiency of today'...
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in all ``sufficiently volatile'' markets. In our formulation, ``sufficientl...
It is shown that an article by C. W. Misner contains serious errors. In particular, the claim that the Yilmaz theory of gravitation cancels the Newtonian gravitational interaction is based on a false premise. With the correct premise the conclusion...
Using pluricomplex Green functions we introduce a compactification of a complex manifold $M$ invariant with respect to biholomorphisms similar to the Martin compactification in the potential theory. For this we show the existence of a norming volume...
We show that the scattering amplitude of four open string scalars or tachyons on the world-volume of a D$_p$-brane in the bosonic string theory can be written in a universal form. The difference between this amplitude and the corresponding amplitud...
This paper presents a trust computation for international relations and its calculus, which related to Bayesian inference, Dempster Shafer theory and subjective logic. We proposed a method that allows a trust computation which is previously subjectiv...
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any help is most welcome. We prove that the restriction of surface minorit...
This work is devoted to the derivation of novel analytic results for special functions which are particularly useful in wireless communication theory. Capitalizing on recently reported series representations for the Nuttall $Q{-}$function and the inc...
We continue to analyze basic constraints on the human decision making from the viewpoint of quantum measurement theory (QMT). As it has been found, the conventional QMT based on the projection postulate cannot account for the combination of the quest...
The purpose of this note is to establish a direct link between the theory of unexpected hypersurfaces and varieties with defective osculating behavior. We identify unexpected plane curves of degree 4 as sections of a rational surface X of degree 7 in...
Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic constructions of f...
In this paper we develop the definition of a global orthogonal spectrum and its unitary version. It relates $G-$equivariant spectra by equivariant weak equivalence in a coherent way. This category of global spectra has a model structure Quillen equiv...
In this thesis, we use some methods of theory of stochastic process to approach turbulence in fluid dynamics. We discuss the Kolmogorov model for fully developed homogeneous turbulence, some recent analytical results to the 1-D Burgers' equation ap...
We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially self-adjoint and F...