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Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer…
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased…
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…
We show unconditional uniqueness of solutions to the Cauchy problem associated with the Benjamin-Ono equation under the periodic boundary condition with initial data given in $H^s$ for $s>1/6$. This improves the previous unconditional…
The framework of joint typical periodic optimization, in which both the dynamical system and the potential function are allowed to vary simultaneously, was introduced in [HHJL25], in a direction motivated by the work of Yang, Hunt & Ott…
We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p\loc(\R^d)$, and with magnetic potentials in ${L^{q}\loc(\R^d)}$, where ${p >…
In this paper, we carry a detailed study of mechanical systems with configuration space $Q\longrightarrow Q/G$ for which the base $Q/G$ variables are being controlled. The overall system's motion is considered to be induced from the base…
We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…
In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…
In this paper, a simple and unified method is developed that predicts the relativistic alterations of physical measures when the behavior of a natural system is characterized by means of a specific operator equation. Separation of variables…
Consider a positive operator $T$ on an $L^p$-space (or, more generally, a Banach lattice) which increases the support of functions in the sense that $supp(Tf) \supseteq supp{f}$ for every function $f \ge 0$. We show that this implies, under…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \[ x^{\Delta}(t)=A(t)x(t)+Q^{\Delta}\left(t,x\left(\delta_{-}(s,t)\right) \right)…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori…
One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…