Composite materials reinforced with a system of three straight,mutually orthogonal fibers

An extension of existing methods of calculating fibrous composites to the case of reinforcement in three mutually perpendicular directions is presented. The basic approach involves the introduction of a "modified" matrix, the properties of which are determined in terms of the elastic moduli of the binder and the reinforcement coefficient in one of the three directions. Approximate expressions are obtained for the elastic characteristics of materials with a high-modulus reinforcing phase. There is a considerable increase in the transverse modulus by comparison with the shear modulus, even for a low reinforcement coefficient in the third direction.     

Structural stresses in composites reinforced with a system of anisotropic fibers

The effect of the anisotropy of the mechanical and thermophysical characteristics of the reinforcement on the temperature stresses in unidirectional composites has been investigated. The stresses near fibers forming a regular structure in the transverse plane are estimated as a function of the thermoelastic properties of the components and the structure parameters.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 728–731, July–August, 1974.     

Triplets of mutually orthogonal circles associated with any ellipse

The author has shown (J. Geom. 94, 159–173, 2009) that, for any general point P on a given ellipse H, four concyclic notable points exist which determine a circle (denoted by Ω) orthogonal to Monge’s circle. Now, it is shown that a new set of notable concyclic points exists; such points determine a circle (denoted by Δ) orthogonal to both Monge’s circle and the circle Ω. Moreover, it is possible to introduce a new ellipse (denoted by H _Δ) concentric with the circle Δ, which is tangent to the ellipse H at P, shares the same circle Ω with the ellipse H and admits the circle Δ as its own Monge’s circle. Only elementary facts from trigonometry and analytic geometry are used.     

Graphs with three mutually pseudo-similar vertices

Vertices u and v of a graph X are pseudo-similar if X ? u ? X ? v but no automorphism of X maps u to v. We describe a group-theoretic method for constructing graphs with a set of three mutually pseudo-similar vertices. The method is used to construct several examples of such graphs. An algorithm for extending, in a natural way, certain graphs with three mutually pseudo-similar vertices to a graph in which the three vertices are similar is given. The algorithm suggests that no simple characterization of graphs with a set of three mutually pseudo-similar vertices can exist.     

Construction of the mutually orthogonal extraordinary supersquares

Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in $\mathbb{F}_d \times \mathbb{F}_d$ . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups in $\mathbb{F}_d \times \mathbb{F}_d$ are of great importance in the field of quantum information processing, especially for the study of mutually unbiased bases. We determine the most general complete sets of mutually orthogonal extraordinary supersquares of order 4, which consist in the so-called Type I and Type II. The well-known case of d ? 1 mutually orthogonal Latin squares is only a special case, namely Type I.     

Countable linear orders with disjoint infinite intervals are mutually orthogonal

Two linear orderings of a same set are perpendicular if the only self-mappings of this set that preserve them both are the identity and the constant mappings. Two linear orderings are orthogonal if they are isomorphic to two perpendicular linear orderings. We show that two countable linear orderings are orthogonal as soon as each one has two disjoint infinite intervals. From this and previously known results it follows in particular that each countably infinite linear ordering is orthogonal to itself.     

Designs with no three mutually disjoint blocks

Let D(v,b,r,k,λ) be any quasi-symmetric block design with block intersection numbers 0 and y. Suppose D has no three mutually disjoint blocks. We show that for a given value of y, there are only finitely many parameter sets of such designs. Moreover, the ‘extremal’ designs D have one of the following parameter sets: (1) v = 4y, k = 2y, λ = 2y − 1 (y 2) (2) v = y(y²+3y+1), k = y(y+1), λ =y²+y−1(y2) (3) v = (y+1)(y²+2y−1), k = y(y+1), λ =y² (y2) A computer search revealed only three parameter sets in the range 1y199, which are not of the above types.     

Three new constructions of mutually orthogonal latin squares

Let N(n) denote the maximum number of mutually orthogonal Latin squares of order n. It is shown that N(24)≥ 6, N(48) ≥ 7, N(55) ≥ 6. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 218–220, 2000     

Five mutually orthogonal Latin squares of order 35

Let N(n) denote the maximum number of mutually orthogonal Latin squares of order n. It is shown that N(35) ≥ 5. © 1996 John Wiley & Sons, Inc.     

Six mutually orthogonal Latin squares of order 48

A direct construction of six mutually orthogonal Latin squares of order 48 is given. © 1997 John Wiley & Sons, Inc. J Combin Designs 5:463–466, 1997     

On the maximality of a set of mutually orthogonal Sudoku Latin Squares

The maximum number of mutually orthogonal Sudoku Latin squares (MOSLS) of order \(n=m^2\) is \(n-m\). In this paper, we construct for \(n=q^2\), q a prime power, a set of \(q^2-q-1\) MOSLS of order \(q^2\) that cannot be extended to a set of \(q^2-q\) MOSLS. This contrasts to the theory of ordinary Latin squares of order n, where each set of \(n-2\) mutually orthogonal Latin Squares (MOLS) can be extended to a set of \(n-1\) MOLS (which is best possible). For this proof, we construct a particular maximal partial spread of size \(q^2-q+1\) in \(\mathrm {PG}(3,q)\) and use a connection between Sudoku Latin squares and projective geometry, established by Bailey, Cameron and Connelly.     

The enumeration of cyclic mutually nearly orthogonal Latin squares

In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum such that there exists a set of cyclic MNOLS of order for , as well as providing a full enumeration of sets and lists of cyclic MNOLS of order under a variety of equivalences with . This resolves in the negative a conjecture that proposed that the maximum for which a set of cyclic MNOLS of order exists is .     

Designs with mutually orthogonal resolutions and decompositions of edge‐colored graphs

Two resolutions R and R^′ of a combinatorial design are called orthogonal if |R_i∩R|≤1 for all R_i∈R and R∈R^′. A set Q={R¹, R², …, R^d} of d resolutions of a combinatorial design is called a set of mutually orthogonal resolutions (MORs) if the resolutions of Q are pairwise orthogonal. In this paper, we establish necessary and sufficient conditions for the asymptotic existence of a (v, k, 1)‐BIBD with d mutually orthogonal resolutions for d≥2 and k≥3 and necessary and sufficient conditions for the asymptotic existence of a (v, k, k?1)‐BIBD with d mutually orthogonal near resolutions for d≥2 and k≥3. We use complementary designs and the most general form of an asymptotic existence theorem for decompositions of edge‐colored complete digraphs into prespecified edge‐colored subgraphs. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 425–447, 2009     

Properties of fiberglass-plastics reinforced with high-modulus fibers

The question of reinforcement of unidirectional fiberglass-plastic with boron or carbon fibers is considered. Static fatigue curves for the Poisson coefficient and the elastic modulus as functions of the volume content of the glass and the high-modulus fibers have been constructed. The theoretical dependences are compared with the experimental data.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Moscow. Translated from Mekhabika Polimerov, No. 1, pp. 68–74, January–February, 1972.     

Five mutually orthogonal Latin squares of orders 24 and 40

Let N(n) denote the maximum number of mutually orthogonal Latin squares of order n. It is proved that N(24) and N(40)5.     

Algebraic representation of affine MDS-codes and mutually orthogonal Latin squares

An algebraic representation of affine MDS-codes and of mutually orthogonal Latin squares (MOLS) is given by introducing the term of a partial ternary. The extension respectively lengthening of partial ternaries, MDS-codes and MOLS is discussed.     

Polypropylene reinforced with aramid and glass fibers

The effect of the chemical nature of the aramid fibers Phenylone, Terlon, Armos, and SVM on the mechanical, thermophysical, and antifriction properties of reinforced polypropylene was investigated. It was found that the composite filled with SVM fibers based on a stiff-chain polymer has high tensile strength and bending modulus. Reinforcement of polypropylene with Phenylone stiff-chain fibers produces a composite with a high impact viscosity. Organoplastics based on polypropylene and aramid fibers have a low density and friction coefficient and high durability. Reinforcement of polypropylene with aramid (SVM) and glass fibers increases the technological properties of the composites. The glass-filled organoplastics developed can be used in instrument making, radio engineering, and machine building as antifriction and construction materials.Ukrainian State Chemical Technological University, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 106–110, January–February, 1996.     

Structural characteristics of materials reinforced with high-modulus fibers

Research on the mechanics of boron and carbon-reinforced plastics is briefly reviewed. The design and testing characteristics of these materials associated with the high degree of anisotropy of their elastic properties, as compared with those of glass-reinforced plastics, are discussed. Problems relating to testing at an angle to the direction of the reinforcement, the effect of misorientation and distortion of the fibers, and the consequences of the low shear strength are considered. Experimental confirmation has been obtained by testing unidirectional (1 : 0), orthogonally reinforced (1 : 1 and 2 : 1), and tridirectional (1 : 1 : 1 in the 0°, +60°, and –60° directions) boron and carbon-reinforced plastics.DeceasedInstitute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 676–685, July–August, 1971.