It is shown that every locally IDEMPOTENT (locally m-pseudoconvex)Hausdorff algebra A with pseudoconvex von Neumann bornology is a regular (respectively, bornological) inductive limit of metrizable locally m-(kB-convex) subalgebras AB of A. In the case where A, in addition, is sequentially BA-complete (sequentially advertibly complete), then every subalgebraAB is a locally m-(kB-convex) Frechet algebra (respectively, an advertibly complete metrizable locally m-(kB-convex) algebra) for some kB Î (0, 1]. Moreover, for a commutative unital locally m-pseudoconvex Hausdorff algebra A over C with pseudoconvex von Neumann bornology, which at the same time is sequentially BA-complete and advertibly complete, the statements (a)–(j) of Proposition 3.2 are equivalent.

The paper deals with uninorms and nullnorms as basic semi-group operations which are commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In [Kalina 2019], they were introduced on bounded posets. This contribution is a generalization and extension of the results in [Kalina 2019]. Some necessary and some sufficient conditions for the existence of IDEMPOTENT uninorms and IDEMPOTENT nullnorms on bounded posets are studied. Finally, some application examples are provided.

Design methods for paraunitary matrices from complete orthogonal sets of IDEMPOTENTs and related MATRIX structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.

The relations between the spectrum of the MATRIX Q+ Rand the spectra of matrices (g+δ) Q+(a+b) R-QR-RQ, QR-RQ, aRb-QRQ, aRQR-(QR) 2, and bR-QR have been given assuming that the MATRIX Q+R is diagonalizable, where Q, R are {g,δ}-quadratic MATRIX and f; g-quadratic MATRIX, respectively, of order n.

This paper studies the algebraic structure of transposition hypergroups with IDEMPOTENT identity. Their subhypergroups and their properties are examined. Right, left and double cosets are defined through symmetric subhypergroups and their properties are studied. Further-more, this paper examines the homomorphisms, the behaviour of attractive and non-attractive elements through them, as well as the relation of their kernels and images to symmetric subhypergroups.

Recently, Fang and Hu introduced the definition of semi-t-operators on bounded lattices. In this study, we propose several construction methods to obtain such a semi-t-operator from a given semi-t-conorm and semi-t-norm on bounded lattices. Furthermore, we discuss the presence of IDEMPOTENT semi-t-operators on bounded lattices, and show several different methods for construction of IDEMPOTENT semi-t-operators on bounded lattices with additional constraints.

The study of operators satisfying Bishop's property (b) is of significant interest and is currently being done by a number of mathematicians around the world. Recently Uchiyama and Tanahashi [Oper. Matrices 4 (2009), 517–524] showed that a paranormal operator has Bishop's property (b). In this paper we introduce a new class of operators which we call the class of kquasi- paranormal operators. An operator T is said to be a k-quasi-paranormal operator if it satisfies ||Tk+1x||2£||Tk+2x|||Tkx|| for all xÎH where k is a natural number. This class of operators contains the class of paranormal operators and the class of quasi-class A operators. We prove basic properties and give a structure theorem of k-quasi-paranormal operators. We also show that Bishop’s property (b) holds for this class of operators. Finally, we prove that if E is the Riesz IDEMPOTENT for a nonzero isolated point l0 of the spectrum of a k-quasi-paranormal operator T, then E is self-adjoint if and only if the null space of T-l0, ker(T-l0)  ker(T*-`l0).

In this paper, we de ne a generalized of clean of Krasner hyperrings for general hyperrings based on the notation of nilpotent elements of a general hyperring R, named nil clean hyperring. We examine characterization of this kind of hyperrings and  nally, we obtain some relations of nil clean general hyperrings with other hyperrings.

The aim of the present study was the histological evaluation of Enamel MATRIX Derivative (EMD) effectiveness for regeneration of periodontal defects. EMD activates cementum synthesis, PDL and bone during the maturation stage of follicole. In this research, EMD was used in surgical defects of premolar teeth in four adult sheep. Muccoperiosteal flap was reflected in buccal site of teeth. The buccal bone plate was removed from mesial to distal in 4 mm depth. After eliminating the cementum by bur and its etching, EMD was applied on exposed dentine and flap was sutured. In opposite sites of those teeth (control sites) the same process was performed without etching. After 100 days, sheep were sacrificed and histological study through light microscopic was performed on black sections of operation sites. The results showed that in test sites, regeneration of cementum and bone was 62/5% and 42/5-50% respectively. But in control sites regeneration of cementum and bone was 37.5% and 32/5-42/5% respectively. Also the migration of junctional epithelium in control sites was 8-10% more than test sites. The important point is that in test sites, cementum was completely attached to undermining dentine. But, in control sites, the gap between cementum and dentine was visible. As a result, this study suggests that EMD promotes periodontal regeneration, and EMD application is a successful achievement in regenerative periodontal therapy.

Let R be an associative ring with unity. An element aÎR is said to be r-clean if a=e+r, where e is an IDEMPOTENT and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Furthermore, we prove that if 0 and 1 are the only IDEMPOTENTs in R, then an r-clean ring is an exchange ring. Also we show that the center of an r-clean ring is not necessary r-clean, but if 0 and 1 are the only IDEMPOTENTs in R, then the center of an r-clean ring is r-clean. Finally, we give some properties and examples of r-clean rings.