In mathematics the basic operations are addition, subtraction, multiplication and division, a mathematical operator is symbol that used to indicate what operation be realized, for example, +, −, ×, ¸, so on. this article, I present procedure by which it possible reduce any natural number -even or odd, with without decimals-, one of first four odd numbers: 1, 3, 5, 7. suggest >n< reduction...

Operations with tensors, or multiway arrays, have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-1 outer products using either the CANDECOMP/PARAFAC (CP) or the Tucker models, or some variation thereof. Such decompositions are motivated by specific applications where the goal is to find an approximate such representation for ...

We transform the oscillator algebra with κ-deformed multiplication rule, proposed in [1, 2], into the oscillator algebra with κ-deformed flip operator and standard multiplication. We recall that the κ-multiplication of the κ-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with κ-multiplication and with κ-flip operation. On the...

The L-decomposable and the bi-decomposable models are two families of distributions on the set Sn of all permutations of the first n positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these...

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

where the integral in (1.1) should be interpreted in the principal value sense when (ax + b)(ax + d) < 0. Note that for a = 0, Ha,b,d is not a convolution operator. When a = 1, H1,b,d = H(fχ[−d,−b]) is the Hilbert transform composed with multiplication by the characteristic function of the interval [−d,−b]. When a = 0, H0,b,d is a well understood operator. In the sequel, we will concentrate our...

−→ (Ak, φk) and the operator algebras A = lim −→ (Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE = Homu(E⊗K, E⊗K) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is refer...

‎recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎in this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎then we use this construction to generalize the result due to cook and nagel‎.

The optimal robust disturbance rejection problem plays an important role in feedback control theory. Here its time-varying version is solved explicitly in terms of duality and operator theory. In particular, the optimum is shown to satisfy a time-varying allpass property. Moreover, optimal performance is given in terms of the norm of a bilinear form. The latter depends on a lower triangular pro...

For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego’s definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to...