Related papers: New Proofs for Several Properties of Capacities
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
A method for computing lower bounds on capacities of 2-dimensional constraints having a symmetric presentation in either the horizontal or the vertical direction is presented. The method is a generalization of the method of Calkin and Wilf…
We consider two capacity quantities associated with bipartite unitary gates: the entangling and the disentangling power. For two-qubit unitaries these two capacities are always the same. Here we prove that these capacities are different in…
In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.
This note reviews prospects for quantum computing. It argues that gates need to be tested for a wide range of probability amplitudes.
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…
Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We…
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…
We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
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…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
In this paper, we study additional aspects of the capacity distribution on the set $\mathcal{B}_n$ of compositions of $n$ consisting of $1$'s and $2$'s. Among our results are further recurrences for this distribution as well as formulas for…
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
In this paper, we will study p-adic q-expansion of alternating sums of powers. From these properties, we derive some interesting properties related to p-adic q-expansion of alternating sums of powers
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
In this work we develop some categorical aspects of the double structure of a module.
After a short review of some basic facts on g-frames, we analyze in details the so-called (alternate) dual g-frames. We end the paper by introducing what we call {\em g-coherent states} and studying their properties.
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…