Sanaa El Assar - Academia.edu (original) (raw)

Papers by Sanaa El Assar

Research paper thumbnail of Quasi-modular Pseudo-Complemented Semi-lattices

In this paper we dene and introduce a new class of pseudocomplemented semilattices ; the class of... more In this paper we dene and introduce a new class of pseudocomplemented semilattices ; the class of quasi-modular pseudocomplemented semilattices; which generalizes modular pseudocomplemented semilattices.We give a characterization and a construction of such class, using a triple containing a Boolean algebra, a semilattice with a greatest element and a structure map. We describe homomorphisms, subalgebras and congruence relations of the quasi-modular pseudo-complemented semi-lattices by means of triples.

Research paper thumbnail of Congruence Pairs of Decomposable MS-Algebras

Chinese Annals of Mathematics, Series B, 2021

In this paper, the authors first introduce the concept of congruence pairs on the class of decomp... more In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras (see [13]). They show that every congruence relation θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1,θ2), where θ1 is a congruence on the de Morgan subalgebra L°° of L and θ2 is a lattice congruence on the sublattice D(L) of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.

Research paper thumbnail of Electrical and optical characterization of SiONC dielectric thin film deposited by polymer-source chemical vapor deposition

Journal of Applied Physics, 2007

In c-Si solar cells, surface recombination velocity increases as the wafer thickness decreases du... more In c-Si solar cells, surface recombination velocity increases as the wafer thickness decreases due to an increase in surface to volume ratio. For high efficiency, in addition to low surface recombination velocity at the rear side, a high internal reflection from the rear surface is also required. The SiO x N y film with low absorbance can act as rear surface reflector. In this study, industrially feasible SiO 2 /SiO x N y stack for rear surface passivation and screen printed local aluminium back surface field were used in the cell structure. A 3 nm thick oxide layer has resulted in low fixed oxide charge density of 1.58 Â 10 11 cm À2 without parasitic shunting. The oxide layer capped with SiO x N y layer led to surface recombination velocity of 155 cm/s after firing. Using single layer (SiO 2) rear passivation, an efficiency of 18.13% has been obtained with V oc of 625 mV, J sc of 36.4 mA/cm 2 and fill factor of 78.7%. By using double layer (SiO 2 /SiO x N y stack) passivation at the rear side, an efficiency of 18.59% has been achieved with V oc of 632 mV, J sc of 37.6 mA/ cm 2 , and fill factor of 78.3%. An improved cell performance was obtained with SiO 2 /SiO x N y rear stack passivation and local BSF.

Research paper thumbnail of P-algebras with Stone congruence lattices

/7-algebras with Stone congruence lattices T. KATRINAK and S. EL-ASSAR 1. Introduction. In [12] w... more /7-algebras with Stone congruence lattices T. KATRINAK and S. EL-ASSAR 1. Introduction. In [12] we have described by means of subdirect factorization congruence distributive algebras A whose congruence lattices Con (A) are atomic, Boolean, or Stonean. The purpose of this paper is to give an intrinsic characterization of those quasi-modular /»-algebras whose congruence lattices are atomic, Stonean or relatively Stonean. To obtain this we use the representation of congruence relations of quasi-modular /»-algebras in terms of congruence pairs. That means (see [11]), that every congruence relation a£Con (L) of a quasi-modular /»-algebra L can be uniquely represented by a congruence pair (a B , a D), where a B is a (Boolean) congruence relation of B(L) and a D a (lattice) congruence relation of D(L). We start with a description of congruence pairs corresponding to (relative) pseudocomplements in the lattice Con (L) (Theorem 1). By way of application, we characterize those quasi-modular /»-algebras with atomic congruence lattices (Theorems 2, 3 and 4). As a second application we provide a characterization of (rejative) Stone congruence lattices of quasi-modular p-algebras (Theorems 5, 6 and 11): Analogous, but deeper results, are obtained for distributive /»-algebras (Theorems 7, 8 and 12). 2. Preliminaries. A (modular, distributive) p-algebra or pseudocomplemented lattice is an algebra (L; V, A, *, 0,1) in which the deletion of the unary operation * yields a bounded (modular, distributive) lattice and * is the operation of pseudocomplementation, that is, xSa* if and only if aAx=0. A /»-algebra is said to be quasi-modular if it satisfies the identity [{xKy)V = (xAjOV(z**Ax). The variety of quasi-modular /»-algebras properly contains the class of modular /»-algebras and is properly contained in the class of /»-algebras satisfying the identity x = x**A(x\\/x*).

Research paper thumbnail of Quasi-modular Pseudo-Complemented Semi-lattices

In this paper we dene and introduce a new class of pseudocomplemented semilattices ; the class of... more In this paper we dene and introduce a new class of pseudocomplemented semilattices ; the class of quasi-modular pseudocomplemented semilattices; which generalizes modular pseudocomplemented semilattices.We give a characterization and a construction of such class, using a triple containing a Boolean algebra, a semilattice with a greatest element and a structure map. We describe homomorphisms, subalgebras and congruence relations of the quasi-modular pseudo-complemented semi-lattices by means of triples.

Research paper thumbnail of Congruence Pairs of Decomposable MS-Algebras

Chinese Annals of Mathematics, Series B, 2021

In this paper, the authors first introduce the concept of congruence pairs on the class of decomp... more In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras (see [13]). They show that every congruence relation θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1,θ2), where θ1 is a congruence on the de Morgan subalgebra L°° of L and θ2 is a lattice congruence on the sublattice D(L) of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.

Research paper thumbnail of Electrical and optical characterization of SiONC dielectric thin film deposited by polymer-source chemical vapor deposition

Journal of Applied Physics, 2007

In c-Si solar cells, surface recombination velocity increases as the wafer thickness decreases du... more In c-Si solar cells, surface recombination velocity increases as the wafer thickness decreases due to an increase in surface to volume ratio. For high efficiency, in addition to low surface recombination velocity at the rear side, a high internal reflection from the rear surface is also required. The SiO x N y film with low absorbance can act as rear surface reflector. In this study, industrially feasible SiO 2 /SiO x N y stack for rear surface passivation and screen printed local aluminium back surface field were used in the cell structure. A 3 nm thick oxide layer has resulted in low fixed oxide charge density of 1.58 Â 10 11 cm À2 without parasitic shunting. The oxide layer capped with SiO x N y layer led to surface recombination velocity of 155 cm/s after firing. Using single layer (SiO 2) rear passivation, an efficiency of 18.13% has been obtained with V oc of 625 mV, J sc of 36.4 mA/cm 2 and fill factor of 78.7%. By using double layer (SiO 2 /SiO x N y stack) passivation at the rear side, an efficiency of 18.59% has been achieved with V oc of 632 mV, J sc of 37.6 mA/ cm 2 , and fill factor of 78.3%. An improved cell performance was obtained with SiO 2 /SiO x N y rear stack passivation and local BSF.

Research paper thumbnail of P-algebras with Stone congruence lattices

/7-algebras with Stone congruence lattices T. KATRINAK and S. EL-ASSAR 1. Introduction. In [12] w... more /7-algebras with Stone congruence lattices T. KATRINAK and S. EL-ASSAR 1. Introduction. In [12] we have described by means of subdirect factorization congruence distributive algebras A whose congruence lattices Con (A) are atomic, Boolean, or Stonean. The purpose of this paper is to give an intrinsic characterization of those quasi-modular /»-algebras whose congruence lattices are atomic, Stonean or relatively Stonean. To obtain this we use the representation of congruence relations of quasi-modular /»-algebras in terms of congruence pairs. That means (see [11]), that every congruence relation a£Con (L) of a quasi-modular /»-algebra L can be uniquely represented by a congruence pair (a B , a D), where a B is a (Boolean) congruence relation of B(L) and a D a (lattice) congruence relation of D(L). We start with a description of congruence pairs corresponding to (relative) pseudocomplements in the lattice Con (L) (Theorem 1). By way of application, we characterize those quasi-modular /»-algebras with atomic congruence lattices (Theorems 2, 3 and 4). As a second application we provide a characterization of (rejative) Stone congruence lattices of quasi-modular p-algebras (Theorems 5, 6 and 11): Analogous, but deeper results, are obtained for distributive /»-algebras (Theorems 7, 8 and 12). 2. Preliminaries. A (modular, distributive) p-algebra or pseudocomplemented lattice is an algebra (L; V, A, *, 0,1) in which the deletion of the unary operation * yields a bounded (modular, distributive) lattice and * is the operation of pseudocomplementation, that is, xSa* if and only if aAx=0. A /»-algebra is said to be quasi-modular if it satisfies the identity [{xKy)V = (xAjOV(z**Ax). The variety of quasi-modular /»-algebras properly contains the class of modular /»-algebras and is properly contained in the class of /»-algebras satisfying the identity x = x**A(x\\/x*).