For a given measure space (X, B, m) we construct all measure spaces (Y, C, l) in which (X, B, m) is embeddable. The construction is modeled on the ultrafilter construction of the Stone-Cech compactification of a completely regular topological space.Under certain conditions the construction simplifies. Examples are given when this simplification occurs.

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper we compute the lower bound for dilation and congestion of embedding onto wheel-like networks. Further, we compute the exact dilation of embedding wheellike networks into hypertrees, proving that the lower bound obtained is sharp. Again, we compute the exact congestion of embedding windmill graphs into circulant graphs, proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding wheels and fans into 1, 2-fault hamiltonian graphs. Using this we estimate the exact wirelength of embedding wheels and fans into circulant graphs, generalized Petersen graphs, augmented cubes, crossed cubes, Möbius cubes, twisted cubes, twisted n-cubes, locally twisted cubes, generalized twisted cubes, odd-dimensional cube connected cycle, hierarchical cubic networks, alternating group graphs, arrangement graphs, 3-regular planer hamiltonian graphs, star graphs, generalised matching networks, fully connected cubic networks, tori and 1-fault traceable graphs.

In the image stegenography, the distortion of stego image will be increased by increasing the number of embedded bits and this makes the enemy be much more suspicious about the existence of secret information in the images. One can use the matrix embedding technique to alleviate this problem which can be done by dividing the cover image into some blocks and limiting the changes in each block. However, the embedding capacity will be limited by this technique. In this article, a solution to this problem (limited embedding capacity), a modified version of Fan’s method, is presented. In this technique, the maximum number of changes in each block is chosen to be 2 instead of 1 in Fan’s technique which leads to reducing the blocks length and increasing the embedding capacity. The results revealed that for a given capacity, the stego image distortion is decreased and the embedding capacity is increased in compared with the other existing methods in this field. Also, the stego images have high PSNR along with high vision quality which leads to more security.

Purpose: The aims of the paper are to obtain necessary and sufficient conditions of existence and smoothness for non-polynomial spline spaces of fifth order, to establish the uniqueness of the Bφ-spline spaces in the class C4 among mentioned spaces (under condition of fixed grid), and to prove the embedding of the Bφ-spline spaces corresponding to embedded grids.Methods: In the paper, the approximation relations with initial grid and with complete chain of vectors are applied to obtain the minimal spline spaces. Usage of locally orthogonal chain of vectors gives opportunity to construct special approximation relations from which the initial space of Bφ splines is constructed.Results: Deletion of a knot from initial grid gives a new grid, and as result, a new space of Bφ splines is embedded in the initial space mentioned above.Conclusions: Consequent deletion of the knots (one by one) generates the sequence of the embedded spaces of Bφ splines. Obtained results are successfully proved. They may be applied to spline-wavelet decompositions.

Letf ¹1; 3 be a positive integer. We prove that there exists a numerical semigroup S with embedding dimension three such that f is the Frobenius number of S. We also show that the same fact holds for affine semigroups in higher dimensional monoids.

One of the most important parameters in dynamic analysis and design of structures is the lateral displacements caused by loading and incitement instigations to the structure which is very important in the process of computation calculation and determination of the structure sections and dynamic parameters of the structure. In the past, in the process stage of structural analysis and determination of forces and stresses tensions and the response of the structure to existing investigations stimulus, soil and foundation and structure systems were investigated and studied and analyzed with districted and separated forms and numerous great simplifications. These studies were modeled and analyzed by with considering consideration of placing the structure on a rigid solid foundation on a soil with sufficient resistance to resist the session’ s summits and forces, which is transmitted from the structural foundation of the structure to it. Field studies and the results and observations obtained by from visiting the damaged and damaged areas of the earthquake, showed that, even at a certain location and among similar structures for in terms of shape and geometry and dynamic characteristics, the damage caused by the earthquake can could be very different, and this can only be due to the effect attributed to the impact of structure interaction-soil and foundation and such as that. The next Subsequent studies showed that the interaction of soil and foundation and structure themselves are highly strongly influenced by many parameters such as environmental factors, mechanical properties of material and soil, and the seismic characteristics form of foundation and gender, and the depth of soil and substrate seismicity of the zoning of the site of the structure and the geotechnical characteristics of the structure specifications and the like. In this study research, it tries by investigating of the is attempted to investigate these two parameters and modeling it them in the powerful software “ Abaqus” software and considering the sufficient taking into account the number of required models needed that in each of them, One of the parameters under investigation changes, the value of their effect on the dynamic response of the structures are should be studied.

The effects of using both directions and directional subdividing on adaptive grid-embedding on the computational time and the number of grid points required for the same accuracy are considered. Directional subdividing is used from the beginning of the adaptation procedure without any restriction. To avoid the complication of unstructured grid, the semi-structured grid was used. It is used to solve three test cases, transonic and supersonic in viscid flows in channels with circular arc bump and with convergent part. The Euler equations are integrated to steady state by an explicit, finite volume, Ni’s Lax-Wendroff type. In this work, multi-grid technique is applied to increase the convergence rate. The directional subdividing is more complex than both directions subdividing. However, the results show that for the same accuracy, directional subdividing considerably reduces the number of grid points and the computational time.

The aim of phishing is tracing the users's private information without their permission by designing a new website which mimics the trusted website. The specialists of information technology do not agree on a unique definition for the discriminative features that characterizes the phishing websites. Therefore, the number of reliable training samples in phishing detection problems is limited. Moreover, among the available training samples, there are abnormal samples that cause classification error. For instance, it is possible that there are phishing samples with similar features to legitimate ones and vice versa. A supervised feature extraction method, called weighted feature line embedding, is proposed in this paper to solve these problems. The proposed method virtually generates training samples by utilizing the feature line metric. Hence, it can solve the small sample size problem. Moreover, by assigning appropriate weights to each pair of feature points, it corrects the undesirable quality of abnormal samples. The features extracted by our method improve the performance of phishing website detection specially by using small training sets.