modern research physics

---

Some boundary value problems for the Cauchy-Riemann equation with non-local boundary conditions in several regions of plane have been investigated and solved by authors. In this paper, by making use of fundamental solutions of Cauchy-Riemann equations and by presenting analytic solutions to the above-mentioned boundary value problems, we try to present an analytic expression for the solution of Cauchy-Riemann equation in the first semi-quarter.

---

A direct method to determine numerical solutions of linear Volterra integro-differential equations is presented in this paper.. This method is based on block-pulse functions and its operational matrix. By using this approach, the integro-differential equation reduces to a linear lower triangular system of algebraic equations which can be solved easily. Some numerical examples are provided to illustrate accuracy and computational efficiency of the method. MSC: 45J05 41A30

---

Boundary value problems (BVPs) are one of the most important fields in engineering and mathematical physics. In self-adjoint case of these problems, there are some facilities to solve them, such as
eigenvalues of adjoint equations are real numbers and associated eigenfunctions make an orthogonal
basis system.
In this paper a new method for investigation of self-adjoint B.V.Ps including ordinary differential
equations (O.D.Es) is introduced. Based on this method, at first, some necessary conditions
are obtained by making use of fundamental solutions of adjoint equations. Then an algebraic system is made by this necessary conditions and boundary conditions of given boundary value problem.
Finally, by making use of Lagrangian identity and boundary values of unknown function, sufficient conditions for having a self-adjoint problem are presented.

---

The Alut granitoid complex is located in the northwestern part of the Sanandaj–Sirjan zone. This complex comprises three main units i.e. monzogranite to granodiorite bodies (SiO2 = 65–77 wt %) which is widespread throughout the area, a quartz-diorite to tonalite unit (SiO2 = 52–63 wt %) exposed as two stocks and mylonitic granitoid scattered as separate outcrops through the area. NE-SW trending microquartz-diorite and NW-SE trending aplite dykes are also present in this complex. The quartz-diorite to tonalite unit has relatively high CaO,FeO, MgO, Al2O3 and low Rb/Sr, Sr/Y, and (La/Yb)N, which preclude an origin of variably fractionated mantle melts and favour a mafic lower crustal source. Dehydration melting of biotite-bearing metasedimentary sources at relatively low pressures is proposed for the origin of monzogranite to granodiorite unit. Geochemically this complex is metaluminous to slightly peraluminous, typical of I-type granites. It belongs to low K (and high K for some monzogranite samples) calc-alkaline series and displays the geochemical characteristics typical of volcanic arc plutons related to an active continental margin area (e.g. significant Nb, Ti, P and Sr depletion). Based on collected geochemical data, the Alut granitoids originated by partial melting of crustal protoliths having different compositions in a deformed active margin.

---

In this papear, we produce the method for formation and recognizing boundary layers in singular perturbation problems. This method involves four step for localization of non-local boundary conditions to local case.For the given problem some sufficient and necessary conditions are given for formation and non formation of boundary layers. Since the existence of boundary layers and their places has a direct relation with the structure of approximate solutions and uniform solutions, therefore the main purpose of this paper is recognition and formation of boundary layers in singular perturbation problems with non-local boundary conditions. This process will be done by using fundamental solution of adjoint given differential equation and necessary conditions.In fact by using these necessary conditions and given boundary conditions, we make an algebraic system.By solving this algebraic system by Cramer rule we obtain boundary values of unknown function.These values of unknown function are local boundary conditions.The mathematical model for this kind of problem usually is in the form
of either ordinary differential equations (O.D.E) or partial differential equations (P.D.E) in which the highest derivative is multiplied by some powers of as a positive small parameter.

---

This paper aimed to investigate the relation between the coherent states and the wavelets. So first the standard, generalized and nonlinear coherent states were reviewed and then their properties were presented. As an example of the nonlinear coherent states, the coherent states of a two-dimensional harmonic oscillator on a flat space were examined. Using the Dirac notation, the admissibility condition of the mother wavelets was studied. Then by means of the resolution of the identity of the generalized coherent states and the admissibility condition of the wavelets, a systematic method was presented to calculate the polynomial wavelets. At the end, as an illustrative example, the polynomial wavelets were constructed by using the nonlinear coherent states on a flat space.

---

The various species of Alveolina for biostratigraphy of Eocene sedimentary rocks are very important. In this research, the species of Alveolina  are reported for the first time in three cross sections: Chalonak, Kalaterood and East Beinabad. These sections are attributes to Early- Middle Eocene age. The 55 samples collected from Chalonak section and the thickness is reached to 245 m. In this section, four biozones are distinguished. They are following: Alveolina globula-Alveolina solida interval range zone, Alveolina solida-A .globosa interval range zone, Alveolina globusa total range  zone and  Alveolina aragonesis  total range zone. On the basis of index fossils such as  Alveolinana  avellana, A. aragonensis,A. globula, A. leupoldi, A. globusa, A. elliptica nutalli, A. rotundata, A. corbarica, A.solida, which are existing in these biozones, the age of this section is attributed to Early Eocene. Of course two species of Nummulites (Nummulites globulus, N. atacicus) and Cuvilierina valensis are determined in Chalonak section. The 80 samples are collected from Kalaterood section and the thickness is reached to 242 m. In this section, four biozones are distinguished. They are following: Alveolina solida- A. globosa interval range zone, Alveolina globosa total range zone, Alveolina aragonensis-A. canavarii interval range zone and A. canavarii total range zone. The several index fossils are found in this section following: Alveolina aragonensis, A. decipiens, A. Avellana, A. laxa, A. pasticillata, A. canavari, A . globosa and A. solida. The age of this section is Early Eocene.  The 150 samples are collected from East Binabad section and the thickness is reached to 900 m. In this section, four biozones are presented. They are Glomalveolina   lepidula – Alveolina solida interval rage zone. Alveolina elliptica nutali- Alveolina corbarica interval range zone, Alveolina corbarica total range zone and Alveolina ruetimeyeri-Alveolina levantina assemblage zone. There are several index fossils such as Alveolina corbarica, A. elliptica nuttalli, A.levantina,  A. roetimeyeri  and  A. decipiens, Glomalveolina lepidula. The age of this section is early Eocene.

---

In this research work, alpha particle detector is made using semi-insulating GaAs. A surface barrier detector with a semi-insulating GaAs substrate at room temperature with pressure of 10-4 Torr under -particle radiation with 5.48 Mev of Am241 source, have been under investigation. Energy resolution of 2 and 3 mm schottky diameter have been matured and compared with the effect of voltage variation