Abstract:
The paper presents the procedure of limit load calculation of elasto-plastic trusses exposed to the action of proportional load which is gradually increased until the formation of failure mechanism. The calculation is based on the application of static and kinematic theorem of limit analysis which are the basis of the limit analysis of structures which produce the value of the limit load in a quick and efficient manner. Application of these theorems is displayed on the examples of truss girders loaded by one- and twoparameter load.

Abstract:
the present development considers the boundary element method (bem) for the collapse load evaluation of plane strain problems, using the static theorem of the limit analysis. this analysis is based on the rigid-plastic constitutive model, thus requiring a non-linear approach for the boundary element method. normally, non-linear analyses with bems require the use of an auxiliary domain discretization with internal cells. to avoid this domain discretization, the present development makes use of a new non-linear bem approach using a pure boundary discretization recently proposed by noronha & pereira. the results obtained with the new bem approach are compared with results obtained by conventional bem and finite element method (fem). the comparison of the results for the three different approaches is based on the yield function and collapse load values.

A geometrical theorem for the static equilibrium of a
common-point-force system has been proven by means of virtual-work principle:
The equilibrium point of a common-point force system has a minimal weighted
distance summation to every fixed point arbitrarily given on each force line
with a weighing factor proportional to corresponding force value. Especially
the mechanical simulating technique for its inverse problem has been realized
by means of pulley block. The conclusions for the inverse problem derived from
mechanic method are in accordance with that given by the pure mathematical
method, and the self-consistence of the theorem and its inverse problem has
been demonstrated. Some application examples in engineering, economy and
mathematics have been discussed, especially the possible application in the
research of molecular structure, has also been predicted.

Abstract:
Laminated composite shells are frequently used in various engineering applications including aerospace, mechanical, marine, and automotive engineering. This article reviews the recent literature on the static analysis of composite shells. It follows up with the previous work published by the first author [1-4] and it is a continuation of another recent article that focused on the dynamics of composite shells [3]. This paper reviews most of the research done in recent years (2000-2010) on the static and buckling behavior (including postbuckling) of composite shells. This review is conducted with an emphasis on the analysis performed (static, buckling, postbuckling, and others), complicating effects in both material (e.g. piezoelectric) and structure (e.g. stiffened shells), and the various shell geometries (cylindrical, conical, spherical and others). Attention is also given to the theory being applied (thin, thick, 3D, nonlinear …). However, more details regarding the theories have been described in previous work [1,3].

Abstract:
This work presents the results that were obtained in a commercial composting plant where food (149,690 kg) and yard wastes (144,520 kg) were used as raw materials for its stabilization under the aerated static pile (ASP) method as an alternative to the mechanically mixed windrow method to solve problems of flies and odor nuisance complaints.In a pile of approximately 498 m^{3}, the change in temperature was the main parameter that was evaluated during 49 days of positive forced aeration. Subsequently, a part of the material of the ASP (62 m^{3}) was subjected to a curing period for 44 days recording changes in temperature and humidity. The results of carbon dioxide and volatile ammonia emissions analyses(NH_{3})
and of a bioassay to screen for the presence of phytotoxic conditions showed a very mature compost with an emergence > 90% and a seedling vigor > 95%.

Abstract:
English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat’s Last Theorem which had for 358 years notoriously resisted all gallant and spirited efforts to prove it even by three of the greatest mathematicians of all time—such as Euler, Laplace and Gauss. Sir Professor Andrew Wiles’s proof employed very advanced mathematical tools and methods that were not at all available in the known World during Fermat’s days. Given that Fermat claimed to have had the “truly marvellous” proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat’s time, has led many to doubt that Fermat actually did possess the “truly marvellous” proof which he claimed to have had. In this short reading, via elementary arithmetic methods, we demonstrate conclusively that Fermat’s Last Theorem actually yields to our efforts to prove it.

Abstract:
In this work, we study the following problem. , where ？is the
fractional Laplacian and Ω？is a bounded
domain in R^{N}？with Lipschitz
boundary. g: R→R？is an
increasing locally Lipschitz continuous function. and f∈L^{m}(Ω), . We use Stampacchia’s theorem to study existence of
the solution u

Abstract:
First, the numerous claims that the theory of natural selection would be a tautology, just empty circular reasoning, are shown to be erroneous, and that they follow from an essentialistic and deterministic way of thinking, which is not consistent with the dynamic theory of evolution. Secondly, it is proposed that a careful analysis applying Fisher’s Fundamental Theorem of Natural Selection of the seemingly tautologous sentence in question: “those who reproduce most, reproduce most” shows that in actual fact it is a predictive statement. Consequently, the analysis presented reduces the essence of the theory of natural selection to that one single statement.

The virial theorem is written by using the canonical equations of motion in classical mechanics. A moving particle with an initial speed in an n-particle system is considered. The distance of the moving particle from the origin of the system to the final position is derived as a function of the kinetic energy of the particle. It is thought that the considered particle would not collide with other particles in the system. The relation between the final and initial distance of the particle from the origin of the system is given by a single equation.

In this paper, an approach to
Pythagoras’ Theorem is presented within the historical context in which it was
developed and from the underlying intellectual outline of the Pythagorean
School. This was analyzed from a rationalism standpoint. An experiment is
presented to the reader so that they, through direct observation, can analyze
Pythagoras’ Theorem and its relation to the creation of knowledge. The theory
of knowledge conceptualization is used.