In this paper, we introduce the concept of e-small Projective modules as a generlization of Projective modules.

The 2D imaging survey was conducted across an unknown K- 3 cavity that is located in Haditha area-Western Iraq.2D measurements are collected along two intercrossing traverses above the cavity with 105m length of each one. Dipole-dipole array is performed with n-factor of 6 and a-spacing equals to 5m. The inverse models of 2D imaging technique showed clearly that the resistivity contrast between the anomalous part of cavity and background resistivity of rocks is about 800:100 Ωm .In addition, the invers models showed that the depth from ground surface to the upper roof of cavity approximately equals to 11m near the cavity operator. So, the K-3 cavity is well defined from 2D imaging with Dipole –dipole array in comparison with the actua

In projective plane over a finite field q F , a conic is the unique complete
(q 1) arc and any arcs on a conic are incomplete arc of degree less than q 1.
These arcs correspond to sets in the projective line over the same field. In this paper,
The number of inequivalent incomplete k  arcs; k  5,6, ,12, on the conic in
PG(2,23) and stabilizer group types are found. Also, the projective line
PG(1,23) has been splitting into two 12-sets and partitioned into six disjoint
tetrads.

Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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 In a recent study, a special type of plane overpartitions known as k-rowed plane overpartitions has been studied. The function  denotes the number of plane overpartitions of n with a number of rows at most k. In this paper, we prove two identities modulo 8 and 16 for  the plane overpartitions with at most two rows. We completely specify the  modulo 8. Our technique is based on expanding each term of the infinite product of the generating function of the  modulus 8 and 16 and in which the proofs of the key results are dominated by an intriguing relationship between the overpartitions and the sum of divisors, which reveals a considerable link among these functions modulo powers of 2.

In this paper, we introduce the concept of e-small M-Projective modules as a generalization of M-Projective modules.

This study deal with structural and stratigraphic analysis of the seismic reflection data for Hartha Formation at Nasiriyah field, the area of seismic data is about (1237) km2. Nasiriyah oil field is located in Dhi Qar Governorate, southern Iraq, and the oil field is located to the East of Euphrates River of about (38) km northwest of Nasiriyah city. which includes twenty-four (24) wells. In some wells there are oil evidences in Hartha Formation at Nasiriyah oil field, for this reason, Hartha Formation is studied.
Two reflectors are picked (top and bottom Hartha) they are defined by using synthetic seismograms in time domain for wells (Ns-1, and 3). Time and depth of Hartha Formation are drawn using velocity data of reflectors. The st

      Let A, and N  are a semiring ,and  a left A- semimodule, respectively. In this work we will discuss two cases: 

1. The direct summand of π-projective semi module is π-projective, while the direct sum of two π-projective semimodules in general is not π-projective . The details of the proof will be given.
2. We will give a condition under which the direct sum of two π-projective semi modules is π-projective, as well as we also set conditions under which π-projective semi modules are projective.