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In this article, we define three-dimensional q-Riordan arrays and q-Riordan representations for these arrays. Also, we give four cases of infinite multiplication three-dimensional matrices of these arrays. As applications, we obtain three-dimensional qq-Pascal-like matrix and its inverse matrix by Heine’s binomial formula, using combinatorial identities. Finally, we consider the generalization of three-dimensional qq-Pascal-like matrix and give some identities involving qq-binomial coefficients.

There is a number of problems regarding bioengineered structures creation that require further study in the fi eld of regenerative medicine. One of the critical tasks that require solution is the fact that tissue engineered constructions, as a rule, are large, which signifi cantly limits the possibility of diffusion of nutrients and oxygen in them. Thus, the key task of fundamental medicine is to fi nd a technology for restoring the perfusion of the structures created. The article presents a modern overview of the mechanisms of angiogenesis and possible ways of its stimulation during transplantation of tissue engineered constructions.

The problem of integer balancing of a three-dimensional matrix with constraints of second type is studied. The elements of the inner part (all three indices are greater than zero) of the three-dimensional matrix are summed in each direction and each section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements of the inner part with the largest previous or the smallest following integer. At the same time, variations of the sums of elements from those in the initial matrix should be less than 2 and the element with three zero indices should be produced with standard rules of rounding-off. Heuristic algorithms for this problem are suggested in the article: layering algorithm being got as generalization of a similar algorithm for the problem with constraints of first type and a new matrix algorithm. The last one consists of three parts: search for the base matrix, search for the maximal matrix and matrix correcting. Each of them is a cyclic change of the integer matrix using from 1 to 3 elements from the inner part. A modification of the matrix algorithm is suggested. The algorithm is directed to more uniform filling of the inner part of the integer matrix. Also, the complexity of all three algorithms is estimated in the article. The comparative analysis of matrix algorithms based on the results of computing experiments is adduced.

The problem of integer balancing of a three-dimensional matrix with constraints of second type is studied. The elements of the inner part (all three indices are greater than zero) of the three-dimensional matrix are summed in each direction and each section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements of the inner part with the largest previous or the smallest following integer. At the same time variations of the sums of elements from that in the initial matrix should be less than 2 and the element with three zero indices should be produced with standard rules of rounding-off. Some solvability classes for this problem are defined. Also, a model of reducing this problem to a problem of finding the maximum flow in a multiple network and an algorithm for the corresponding flow problem are suggested. A polynomial algorithm for the particular case of n = 2 is described.

The article is devoted to the problem of integer-valued balancing of a three-dimensional matrix. The reduction of this problem to the problem of finding a maximum flow in the multiple network of integer-valued balancing and the algorithm for this problem are suggested. Also, the comparative characteristic of two algorithms of integer-valued bal¬ancing is made according to the results of the computing experiments. NP-completeness of the problem of integer-valued balancing of a three-dimensional matrix is proved in the article. The problem of minimization of the errors of rounding off in the problem of integer-valued balancing is explored.

The article is devoted to the problem of integer-valued balancing of a three-dimensional matrix. A problem of reducing this problem to the problem of finding a maximum flow in network is explored.

The problem of integer balancing of a three-dimensional matrix with constraints of the second type is studied. The elements of the inner part (all three indices are greater than zero) of the three-dimensional matrix are summed in each direction and each section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements of the inner part with the largest previous or the smallest following integer. At the same time, variations of the sums of elements from those in the initial matrix should be less than 2 and an element with three zero indices should be produced with standard rounding-off rules. Heuristic algorithms for this problem are suggested: layering algorithm obtained as a generalization of a similar algorithm for the problem with constraints of the first type and a new matrix algorithm. The latter consists of three parts: search for the basic matrix, search for the maximum matrix, and matrix correction. Each of them is a cyclic change of the integer matrix using from one to three elements from the inner part. A modification of the matrix algorithm is suggested. The algorithm is directed to more uniform filling of the inner part of the integer matrix. Also, the complexity of all three algorithms is estimated. The comparative analysis of matrix algorithms based on the results of computing experiments is adduced. [ABSTRACT FROM AUTHOR]

Background: There is growing interest in the development of cell culture assays that enable the rigidity of the extracellular matrix to be increased. A promising approach is based on three-dimensional collagen type I matrices that are stiffened by cross-linking through non-enzymatic glycation with reducing sugars. Methods: The present study evaluated the biomechanical changes in the non-enzymatically glycated type I collagen matrices, including collagen organization, the advanced glycation end products formation and stiffness achievement. Gels were glycated with ribose at different concentrations (0, 5, 15, 30 and 240 mM). The viability and the phenotypic changes of primary human lung fibroblasts cultured within the non-enzymatically glycated gels were also evaluated along three consecutive weeks. Statistical tests used for data analyze were Mann-Whitney U, Kruskal Wallis, Student's t-test, two-way ANOVA, multivariate ANOVA, linear regression test and mixed linear model. Results: Our findings indicated that the process of collagen glycation increases the stiffness of the matrices and generates advanced glycation end products in a ribose concentration-dependent manner. Furthermore, we identified optimal ribose concentrations and media conditions for cell viability and growth within the glycated matrices. The microenvironment of this collagen based three-dimensional culture induces α-smooth muscle actin and tenascin-C fibroblast protein expression. Finally, a progressive contractile phenotype cell differentiation was associated with the contraction of these gels. Conclusions: The use of non-enzymatic glycation with a low ribose concentration may provide a suitable model with a mechanic and oxidative modified environment with cells embedded in it, which allowed cell proliferation and induced fibroblast phenotypic changes. Such culture model could be appropriate for investigations of the behavior and phenotypic changes in cells that occur during lung fibrosis as well as for testing different antifibrotic therapies in vitro. [ABSTRACT FROM AUTHOR]

The problem of integer balancing of a three-dimensional matrix with constraints of the second type is studied. The elements of the inner part (all three indices are greater than zero) of the three-dimensional matrix are summed in each direction and each section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements of the inner part with the largest previous or the smallest following integer. At the same time variations of the sums of elements from that in the initial matrix should be less than 2 and the element with three zero indices should be produced with standard rules of rounding-off. Some solvability classes for this problem are defined. Also, a model of reducing this problem to a problem of finding the maximal flow in a multiple network and an algorithm for the corresponding flow problem are suggested. A polynomial algorithm for the particular case of n = 2 is described. [ABSTRACT FROM AUTHOR]

Biomaterials are being used for the healthcare applications from ancient times. But subsequent evolution has made them more versatile and has increased their utility. Biomaterials have revolutionized the areas like bioengineering and tissue engineering for the development of novel strategies to combat life threatening diseases. Together with biomaterials, stem cell technology is also being used to improve the existing healthcare facilities. These concepts and technologies are being used for the treatment of different diseases like cardiac failure, fractures, deep skin injuries, etc. Introduction of nanomaterials on the other hand is becoming a big hope for a better and an affordable healthcare. Technological advancements are underway for the development of continuous monitoring and regulating glucose levels by the implantation of sensor chips. Lab-on-a-chip technology is expected to modernize the diagnostics and make it more easy and regulated. other area which can improve the tomorrow's healthcare is drug delivery. Micro-needles have the potential to overcome the limitations of conventional needles and are being studied for the delivery of drugs at different location in human body. There is a huge advancement in the area of scaffold fabrication which has improved the potentiality of tissue engineering. Most emerging scaffolds for tissue engineering are hydrogels and cryogels. Dynamic hydrogels have huge application in tissue engineering and drug delivery. Furthermore, cryogels being supermacroporous allow the attachment and proliferation of most of the mammalian cell types and have shown application in tissue engineering and bioseparation. With further developments we expect these technologies to hit the market in near future which can immensely improve the healthcare facilities. [ABSTRACT FROM AUTHOR]

Abstract: Cubic mesoporous structures with Ia3d symmetry, such as MCM-48 and large pore Ia3d material (LP-Ia3d), which present different pore size (3.6 and 5.7nm, respectively), have been prepared, characterized and used as drug delivery systems. Ibuprofen and erythromycin have been chosen as drug models for delivery studies. The influence of the pore size at these structures has been studied and the results show that the delivery rate of drugs decreases with the pore size of the matrix. The influence of chemical nature of the pore surface on the delivery process has been also studied. In this case, the hydrophilic pore surface has been modified with hydrocarbon chains (C8 and C18 moieties) and the effect upon drug delivery of hydrophobic drugs like erythromycin has been studied. The results show a noticeable decrease of the delivery rate when the surface of the matrices is modified. [Copyright &y& Elsevier]