We introduce the pseudoparticle operator algebra that generates all Hubbardchain eigenstates from a single reference vacuum. The occurence of only zeromomentum pseudoparticle forward scattering at all energy scales combined with the infinite pseudoparticle-number conservation laws establish this operator basis as the most suitable for dealing with transport properties at finite frequencies. We ...

Multirelations provide a semantic domain for computing systems that involve two dual kinds of nondeterminism. This paper presents relational formalisations of Kleisli, Parikh and Peleg compositions and liftings of multirelations. These liftings are similar to those that arise in the Kleisli category of the powerset monad. We show that Kleisli composition of multirelations is associative, but ne...

In this paper we give an explicit construction of n × n matrices over finite fields which are somewhat rigid, in that if we change at most k entries in each row, its rank remains at least Cn(logq k)/k, where q is the size of the field and C is an absolute constant. Our matrices satify a somewhat stronger property, we which explain and call “strong rigidity.” We introduce and briefly discuss str...

ABSTRACT: In this paper, a complete construction of quaternary complex Hadamard matrices of order 2 n is obtained using the method of Sylvester construction and Williamson construction. Williamson construction has been generalized to obtain any kind of Hadamard matrices (Complex or Real Numbers). Non-equivalent family of Hadamard Matrices can be obtained using the Generalized Williamson constru...

The main purpose of this work is to construct the forward and backward solution space of a nonregular discrete time AR-representation i.e. A(σ)ξ(k) = 0, in a closed interval [0, N ] where A(σ) is a polynomial matrix and σ is the forward shift operator. The construction of the behavior is based on the structural invariants of the polynomial matrix which describe the AR-representation, i.e. the f...

I present numerical methods for the computation of stable and unstable manifolds in autonomous dynamical systems. Through differentiation of the Lyapunov-Perron operator in [1], we find that the stable and unstable manifolds are boundary value problems on the original set of differential equation. This allows us to create a forward-backward approach for manifold computation, where we iterativel...

Casting a geophysical inverse problem into Bayesian setting is often discouraged by the computational workload needed to run many forward modelling evaluations. Here we present probabilistic inversions of electrical resistivity tomography data in which operator replaced trained residual neural network that learns non-linear mapping between model and apparent values. The use this specific archit...

From the assumption that there is a measurable cardinal κ with o(κ) = κ, we produce a model in which for all x ⊆ אω, HODx does not contain the powerset of אω. We also prove that this assertion requires large cardinals.

Functors which are determined, up to natural isomorphism, by their values on objects, are called DVO (Defined by Values on Objects). We focus on the collection of polynomial functors on a category of sets (classes), and we give a characterization theorem of the DVO functors over such collection of functors. Moreover, we show that the (κ-bounded) powerset functor is not DVO.