The purpose of this article is to partition PG(3,11) into orbits. These orbits are studied from the view of caps using the subgroups of PGL(4,11) which are determined by nontrivial positive divisors of the order of PG(3,11). The τ_i-distribution and c_i-distribution are also founded for each cap.

   The aim of this paper is to construct the (k,r)-caps in the projective 3-space PG(3,p) over Galois field GF(4). We found that the maximum complete (k,2)-cap which is called an                       ovaloid  , exists in PG(3,4) when k = 13. Moreover the maximum (k,3)-caps, (k,4)-caps and   (k,5)-caps. 

Let be a unitary left R-module on associative ring with identity. A submodule of is called -annihilator small if , where is a submodule of , implies that ann( )=0, where ann( ) indicates annihilator of in . In this paper, we introduce the concepts of -annihilator-coessential and - annihilator - coclosed submodules. We give many properties related with these types of submodules.

 

Experimental work has been performed on three capillary tubes of different lengths and diameters using R-12 and R-134a. The test also studies the effect of discharge and speed of evaporator fan. The results clearly showed that refrigerant type and discharge significantly influence the temperature drop across the capillary tube. While the speed of evaporator fan has small effect. Experimental results showed that the temperature gradient for the two refrigerants are the same, but after approximatly one meter the temperature gradient of R-134a  is steeper than R-12.

 

Let R be a commutative ring with unity. Let W be an R-module, for K≤F, where F is a submodule of W and K is said to be R-annihilator coessential submodule of F in W (briefly R-a-coessential) if  (denoted by K  F in W). An R-module W is called strongly hollow -R-annihilator -lifting module (briefly, strongly hollow-R-a-lifting), if for every submodule F of W with  hollow, there exists a fully invariant direct summand K of W such that K  F in W. An R - module W is called strongly R - annihilator - ( hollow - lifting ) module ( briefly strongly R - a - ( hollow - lifting ) module ), if for every submodule F of W with   R - a - hollow, there exists a fully invariant direct summand K o

    In this work, we construct complete (K, n)-arcs in the projective plane over Galois field GF (11), where 12 2 ≤ ≤ n  ,by using geometrical method (using the union of some maximum(k,2)- Arcs , we found (12,2)-arc, (19,3)-arc , (29,4)-arc, (38,5)-arc , (47,6)-arc, (58,7)-arc, (68,6)-arc, (81,9)-arc, (96,10)-arc, (109,11)-arc, (133,12)-arc, all of them are complete arc in PG(2, 11) over GF(11).  

In this research, we introduce a small essentially quasi−Dedekind R-module to generalize the term of an essentially quasi.−Dedekind R-module. We also give some of the basic properties and a number of examples that illustrate these properties.

An experimental and theoretical works were carried out to model the wire condenser in the domestic refrigerator by calculating the heat transfer coefficient and pressure drop and finding the optimum performance. The two methods were used for calculation, zone method, and an integral method. The work was conducted by using two wire condensers with equal length but different in tube diameters, two refrigerants, R-134a and R-600a, and two different compressors matching the refrigerant type. In the experimental work, the optimum charge was found for the refrigerator according to ASHRAE recommendation. Then, the tests were done at 32˚C ambient temperature in a closed room with dimension (2m*2m*3m). The results showed that th

Let m ≥ 1,n ≥ 1 be fixed integers and let R be a prime ring with char (R) ≠2 and
(m+n). Let T be a (m,n)(U,R)-Centralizer where U is a Jordan ideal of R and T(R)
⊆ Z(R) where Z(R) is the center of R ,then T is (U,R)- Centralizer.