Abstract:
Suppose that $\mathcal{C}$ is the space of all middle Cantor sets. We characterize all triples $(\alpha,~\beta,~\lambda)\in \mathcal{C}\times\mathcal{C}\times \mathbb{R}^*$ that satisfy $C_\alpha- \lambda C_\beta=[-\lambda,~1]. $ Also all triples (that are dense in $\mathcal{C}\times\mathcal{C}\times \mathbb{R}^*$) has been determined such that $C_\alpha- \lambda C_\beta$ forms the attractor of an iterated function system. Then we found a new family of the pair of middle Cantor sets $\mathcal{P}$ in a way that for each $(C_\alpha,~ C_\beta)\in\mathcal{P}$, there exists a dense subfield $F\subset \mathbb{R}$ such that for each $\mu \in F$, the set $C_\alpha- \mu C_\beta$ contains an interval or has zero Lebesgue measure. In sequel, conditions on the functions $f, ~g$ and the pair $(C_\alpha,~C_\beta)$ is provided which $f(C_{\alpha})- g(C_{\beta})$ contains an interval. This leads us to denote another type of stability in the intersection of two Cantor sets. We prove the existence of this stability for regular Cantor sets that have stable intersection and its absence for those which the sum of their Hausdorff dimension is less than one. At the end, special middle Cantor sets $C_\alpha$ and $C_\beta$ are introduced. Then the iterated function system corresponding to the attractor $C_{\alpha}-\frac{2\alpha}{\beta}C_\beta$ is characterized. Some specifications of the attractor has been presented that keep our example as an exception. We also show that $\sqrt{C_{\alpha}}$ - $\sqrt{C_{\beta}}$ contains at least one interval.

Abstract:
In the present paper, We introduce a pair of middle Cantor sets namely $(C_\alpha, C_\beta)$ having stable intersection, while the product of their thickness is smaller than one. Furthermore, the arithmetic difference $C_\alpha- \lambda C_\beta$ contains at least one interval for each nonzero number $\lambda$.

Abstract:
Let $X$ be a topological space. Let $X_0 \subseteq X$ be a second countable subspace. Also, assume that $X$ is first countable at any point of $X_0$. Then we provide some conditions under which we ensure that $X_0$ is not Baire.

Propagation characteristics of low latitude whistler
duct characteristics have been investigated based on day-time measurements at
Jammu. The morphogical characteristics of low latitude whistlers are discussed
and compared with characteristics of middle and high latitude whistlers. The Max. electron
density (N_{m}) at the height
of the ionosphere obtained from whistler dispersion comes out to be higher than
that of the background which is in accordance with the characteristics of
whistler duct. The equivalent width is found to be close to the satellite
observations and the characteristics of whistler duct in low latitude
ionosphere are similar to those in middle and high latitude ionosphere. The
width of ducts estimated from the diffuseness of the whistler track observed
during magnetic storm is found to lie in the range of 50 -200 Km.

Abstract:
Immobilized molecules using biomaterials and nanobiotechnology is a very interesting topic that touching almost all aspects of our life. It uses the sciences of biology, chemistry, physics, materials engineering and computer science to develop instruments and products that are at the cutting edge of some of today’s most promising scientific frontiers. In this review article, the author based on his experience in this arena has tried to focus on some of the supports for im-mobilization; the most important molecules to be immobilized such as DNA, cells, enzymes, metals, polysaccharides, etc and their applications in medicine, food, drug, water treatment, energy and even in aerospace. He specified a special section on what is new in the arena of supports and technologies used in enzyme immobilization and finally a recommendation by the author for future work with a special attention to up-to-date references.

Abstract:
In this work the Generalized Special Relativity (GSR) is utilized to estimate masses of some elementary particles such as, neutrinos. These results are found to be in conformity with experimental and theoretical data. The results obtained may explain some physical phenomena, such as, conversion of neutrinos from type to type when solar neutrino reaches the Earth.

Abstract:
Background: Vacuum-assisted dressing is a noninvasive closure system of the wound, which makes localized and controlled negative pressure. Its mechanical tension reduces edema, stimulates granulation tissue formation and angiogenesis, and prepares the wound bed for closure. In this study, a patient has been presented, who suffered from serious lower extremity wounds due to arterial emboli, one of her wounds has been treated with vacuum-assisted dressing and the other with conventional dressing to evaluate the efficacy of vacuum-assisted dressing in acute ischemic wounds. Methods: A 65-year-old female patient was admitted to the emergency clinic, due to complaint of severe pain in her right lower extremity which suggested an acute arterial occlusion. She immediately underwent an embolectomy operation; however, a few days later, severe ischemia on the leg and foot became appearant. All of the necrosis was sharply debrided under sterile conditions in the operating room, and then lower leg wound was covered with vacuum-assisted dressing, also calcaneal wound was dressed with silver sulphadiazine. Results: Eighteen days after the first dressing with negative pressure, distal leg wound became ready for closure, whereas, enough granulation tissue over the calcaneal area developed merely thirty-four days later. Calcaneal wound closed spontaneously within fifty-three days. Conclusions: When dealing with this experience, using the negative pressure dressing in patient with severe lower limb wounds following arterial emboli, accelerates wound healing by means of developing the granulation tissue, and rapidly prepares the wound for closure, so it may reduce the risk of amputation.

In this article, we have effectively used the Numerical
Inversion of Laplace transform to study the time-dependent thin film
flow of a second grade fluid flowing down an inclined plane through a porous
medium. The solution to the governing equation is obtained by using the standard
Laplace transform. However, to transform the obtained solutions from Laplace
space back to the original space, we have used the Numerical Inversion of Laplace
transform. Graphical results have been presented to show the effects
of different parameters involved and to show how the fluid flow evolves with
time.

In this paper, we
propose and analyze some schemes of the integral collocation formulation based
on Legendre polynomials. We implement these formulae to solve numerically
Riccati, Logistic and delay differential equations with variable coefficients.
The properties of the Legendre polynomials are used to reduce the proposed
problems to the solution of non-linear system of algebraic equations using
Newton iteration method. We give numerical results to satisfy the accuracy and
the applicability of the proposed schemes.

Abstract:
Розглянуто застосування запропонованого ран ше методу оц нювання ймов рност потенц йних конфл кт в для системи керування пов тряним рухом. Досл джено властивост методу, наведено проанал зовано результати комп’ютерного моделювання. Application of the method of potential conflicts probability evaluation offered before for air traffic control system is considered. The properties of the method are investigated, results of computer modeling are represented and analyzed. Рассмотрено применение предложенного ранее метода оценки вероятности потенциальных конфликтов для системы управления воздушным движением. Исследованы свойства метода, приведены и проанализированы результаты компьютерного моделирования.