The relevance of convex and non-convex functions in optimization research is well known. Due to the behavior its definition, idea convexity also plays a major role subject inequalities. main concern this paper establish new integral inequalities for newly defined left right interval-valued function on coordinates through pseudo order relation double integral. Some Hermite–Hadamard type product ...

purpose: to report a case who had optic disc duplication, a rare congenital disorder characterized by two well-defined discs in one eye. case report: a 19 months-old child presented with unilateral epiphora in the right eye since birthday. the right eye was smaller than the left eye and mild ptosis was apparent. nasolacrimal duct probing was performed under general anesthesia. the examination r...

Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the simple monoid-valued fields on an atomless ‘space-time’ set. A canonical decomposition of the logarithmic conditionally posive-definite generating functional is c...

We propose the use of pseudo-singular values, which are closely related to singular values but are allowed to have sign, as a convenient approach for developing techniques for the identification and control of large-scale processes. Steady-state controllability can be assessed directly in terms of the pseudo-singular values. It is shown that to control an output disturbance direction with zero ...

We prove that any submodular function f : {0, 1}n → {0, 1, ..., k} can be represented as a pseudoBoolean 2k-DNF formula. Pseudo-Boolean DNFs are a natural generalization of DNF representation for functions with integer range. Each term in such a formula has an associated integral constant. We show that an analog of Håstad’s switching lemma holds for pseudo-Boolean k-DNFs if all constants associ...

We study solvability for a model elliptic pseudo-differential equation with an additional integral condition in Sobolev–Slobodetskii spaces certain conical domains Euclidean space. . Using the wave factorization symbol we construct solution this boundary value problem and behavior of when parameters cones tend to their extremal values. It was shown that such need besides presented condition.

We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct (Theorem 1) local normal forms of such metrics. We show that these metrics have certain useful properties similar to those of Riemannian Liouville metrics, namely: • they admit geodesically equivalent metrics (Theorem 2); • one can use th...

A three-dimensional (3-D) inversion scheme for fixedoffset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air–soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function for a two-layer medium. The forward model is inverted using the Tikhonov-regularized pseudo-inverse ...