In this paper, we characterize w -Noetherian rings and SM rings. More precisely, in terms of the id="M3"> u -operation on a commutative ring id="M4"> R , prove that id="M5"> is id="M6"> if only direct limit id="M7"> r GV -torsion-free injective id="M8"> -modules id="M9"> SM, whic...

We introduce some constructions of weakly distance-regular digraphs of girth 2, and prove that a certain quotient digraph of a commutative weakly distance-transitive digraph of girth 2 is a distancetransitive graph. As an application of the result, we obtain some examples of weakly distanceregular digraphs which are not weakly distance-transitive. Moreover, a class of commutative weakly distanc...

A one-way permutation (OWP) is one of the most fundamental cryptographic primitives, and can be used as a building block for most of basic symmetric-key cryptographic primitives. However, despite its importance and usefulness, previous black-box separation results have shown that constructing a OWP from another primitive seems hopeless, unless building blocks already achieve “one-way” property ...

In this presentation a technique for constructing bent functions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd dimension. This type of functions yield the first k...

The (in)equational properties of the least fixed point operation on ( -)continuous functions on ( -)complete partially ordered sets are captured by the axioms of (ordered) iteration algebras, or iteration theories. We show that the inequational laws of the sum operation in conjunction with the least fixed point operation in continuous additive algebras have a finite axiomatization over the ineq...

It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this short paper, we first study the global convergence of a sequential injective algorithm for weakly univalent vector equation. Then, we apply the convergence analysis to the regularized smooth...

A generalization of injective modules (noted GI-modules), distinct from p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized. If M is a left GI-module, E = End(AM), then E/J(E) is von Neumann regular, where J(E) is the Jacobson radical of the ring E. A is semisimple Artinian if, and only if, every left A-module is GI. If A is a left p. p., left GI-ring su...

Given two Banach spaces X and Y, we analyze when the projective tensor product X?ˆ?Y has Corson's property (C) or is weakly Lindelöf determined (WLD), subspace of a compactly generated (WCG) space Hilbert space. For instance, show that: (i) WLD if only both Y are all operators from to Y? X? have separable range; (ii) WCG same holds for under assumption that every operator compact; (iii) ?p(?)?ˆ...