Related papers: A note on Khabibullin's conjecture for integral in…

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.

The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…

It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This…

In this paper some Hadamard_type inequalities for product of convex functions of 2-variables on the co-ordinates are given.

In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.

The quantum modularity conjecture, first introduced by Don Zagier, is a general statement about a relation between $\mathfrak{sl}_2$ quantum invariants of links and 3-manifolds at roots of unity related by a modular transformation. In this…

We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…

Two geometric inequalities are established for Einstein totally real submanifolds in a complex space form. As immediate applications of these inequalities, some non-existence results are obtained.

In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…

A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of…

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.

An interplay between the sum of certain series related to Harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits…

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…

A multiplicativity conjecture for quantum communication channels is formulated, validity of which for the values of parameter $p$ close to 1 is related to the solution of the fundamental problem of additivity of the channel capacity in…

In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.

We prove a conjecture of Casselman and Shahidi stating that the unique irreducible generic subquotient of a standard module is necessarily a subrepresentation for a large class of connected quasi-split reductive groups, in particular for…

Using the circle method, we count integer points on complete intersections in biprojective space in boxes of different side length, provided the number of variables is large enough depending on the degree of the defining equations and…

We establish a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of M\"{o}bius and divisor functions. Specifically, we prove that the ratios conjecture and an…

Assuming that the two integrals in the Change of Variable Formula for the Riemann integral on the real line are finite, one can rightfully ask if they have equal value. We give a positive answer to this question. The proof is very easy to…