Change in the mechanical properties of human compact bone tissue upon aging

The ultimate tensile strength σ_z, elastic modulus E, maximum deformation ?, and Brinell hardness H_B of human compact bone tissue were determined. The contents of the minerals calcium and phosphorus, nitrogen, and water (relative to mass and volume), as well as the density were studied in the same bone samples. It was found that all the characteristics studied changed with increasing age. It is emphasized that various types of destructive mechanisms are characteristics of different ages.     

On generalizations of network design problems with degree bounds

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1) by handling more complex degree constraints in the minimum spanning tree problem (namely laminar crossing spanning tree), and (2) by incorporating ‘degree bounds’ in other combinatorial optimization problems such as matroid intersection and lattice polyhedra. We give new or improved approximation algorithms, hardness results, and integrality gaps for these problems. Our main result is a (1, b + O(log n))-approximation algorithm for the minimum crossing spanning tree (MCST) problem with laminar degree constraints. The laminar MCST problem is a natural generalization of the well-studied bounded-degree MST, and is a special case of general crossing spanning tree. We give an additive Ω(log ^c m) hardness of approximation for general MCST, even in the absence of costs (c > 0 is a fixed constant, and m is the number of degree constraints). This also leads to a multiplicative Ω(log ^c m) hardness of approximation for the robust k-median problem (Anthony et al. in Math Oper Res 35:79–101, 2010), improving over the previously known factor 2 hardness. We then consider the crossing contra-polymatroid intersection problem and obtain a (2, 2b + Δ ? 1)-approximation algorithm, where Δ is the maximum element frequency. This models for example the degree-bounded spanning-set intersection in two matroids. Finally, we introduce the crossing latticep olyhedron problem, and obtain a (1, b + 2Δ ? 1) approximation algorithm under certain condition. This result provides a unified framework and common generalization of various problems studied previously, such as degree bounded matroids.     

Effect of fillers on the hardness and structural order of polymers

The effect of various finely dispersed filler particles differing in size, structure, and the chemical nature of the surface, on the hardness of one crystalline (polycaproamide) and two amorphous (polystyrene and polymethylmethacrylate) polymers has been experimentally investigated. The observed changes in hardness are related with a change in the structural order of the polymer under the influence of the filler and with the formation of structures of different strength by the fillers in the polymer.Kiev Shevchenko State University. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1077–1081, November–December, 1968.     

Hardness of approximation for orthogonal rectangle packing and covering problems

Bansal and Sviridenko [N. Bansal, M. Sviridenko, New approximability and inapproximability results for 2-dimensional bin packing, in: Proceedings of the 15th Annual ACM–SIAM Symposium on Discrete Algorithms, SODA, 2004, pp. 189–196] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P=NP. We show that similar approximation hardness results hold for several 2- and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asymptotic approximation ratio of any polynomial time approximation algorithm. Our hardness results apply to the most studied case of 2-dimensional problems with unit square bins, and for 3-dimensional strip packing and covering problems with a strip of unit square base.     

Reductions,completeness and the hardness of approximability

In computability and in complexity theory reductions are widely used for mapping sets into sets in order to prove undecidability or hardness results. In the study of the approximate solvability of hard discrete optimization problems, suitable kinds of reductions, called approximation preserving reductions, can also be used to transfer from one problem to another either positive results (solution techniques) or negative results (non-approximability results). In this paper various kinds of approximation preserving reductions are surveyed and their properties discussed. The role of completeness under approximation preserving reductions is also analyzed and its relationship with hardness of approximability is explained.     

On the complexity of deriving position specific score matrices from positive and negative sequences

Position-specific score matrices (PSSMs) have been applied to various problems in computational molecular biology. In this paper, we study the following problem: given positive examples (sequences) and negative examples (sequences), find a PSSM which correctly discriminates between positive and negative examples. We prove that this problem is solved in polynomial time if the size of a PSSM is bounded by a constant. On the other hand, we prove that this problem is NP-hard if the size is not bounded. We also prove hardness results for deriving multiple PSSMs and related problems.     

On the parameterized complexity of short computation and factorization

A completeness theory for parameterized computational complexity has been studied in a series of recent papers, and has been shown to have many applications in diverse problem domains including familiar graph-theoretic problems, VLSI layout, games, computational biology, cryptography, and computational learning [ADF,BDHW,BFH, DEF,DF1-7,FHW,FK]. We here study the parameterized complexity of two kinds of problems: (1) problems concerning parameterized computations of Turing machines, such as determining whether a nondeterministic machine can reach an accept state in steps (the Short TM Computation Problem), and (2) problems concerning derivations and factorizations, such as determining whether a word can be derived in a grammar in steps, or whether a permutation has a factorization of length over a given set of generators. We show hardness and completeness for these problems for various levels of the hierarchy. In particular, we show that Short TM Computation is complete for . This gives a new and useful characterization of the most important of the apparently intractable parameterized complexity classes. Received August 1, 1994     

Remarks on the zeta function of some diagonal hyperelliptic curves

We compute the Jacobi sums and the zeta functions associated to the family of diagonal curves defined over by y²=γx⁵+δ (with γδ≠0), then we prove that their Jacobians are simple. We discuss about the hardness of the associated discrete logarithm problem with respect to known attacks and we show that our family is suitable for cryptographic purpose.     

Influence of friction in material characterization in microindentation measurement

A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter β (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction.     

Some properties of the polypropylene - aluminum system

The effect of composition on the properties (bulk resistivity, hardness, compressive deformation, density, and microstructure) of polypropylene-aluminum specimens has been investigated. The changes are not additively related with the composition. An explanation of the observations is proposed.Riga Lenin Komsomol Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 2, pp. 323–326, March–April, 1971.     

Certain properties of filled partly plasticized polyvinylchloride

The effect of iron oxide as a filler for hard partly plasticized polyvinylchloride was studied. It was shown that the influence of iron oxide on polymer properties varies depending on the proportion of the filler used. When added in small quantities, it improves certain physico-mechanical properties of polyvinylchloride, such as, for instance, its hardness and wear resistance.Mekhanika Polimerov, Vol. 2, No. 6, pp. 813–816, 1966     

Inapproximability of Edge-Disjoint Paths and low congestion routing on undirected graphs

In the undirected Edge-Disjoint Paths problem with Congestion (EDPwC), we are given an undirected graph with V nodes, a set of terminal pairs and an integer c. The objective is to route as many terminal pairs as possible, subject to the constraint that at most c demands can be routed through any edge in the graph. When c = 1, the problem is simply referred to as the Edge-Disjoint Paths (EDP) problem. In this paper, we study the hardness of EDPwC in undirected graphs.     

The longest common subsequence problem for arc-annotated sequences

Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The

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problem has recently been introduced in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in: Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280] as a framework for studying the similarity of arc-annotated sequences. In this paper, we consider arc-annotated sequences with various arc structures and present some new algorithmic and complexity results on the problem. Some of our results answer an open question in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in: Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280] and some others improve the hardness results in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280].     

Optimization of technology parameters for the plane-strain component in the process of gas quenching

The paper introduces an optimization method for the technology parameters of the plane-strain component in the process of gas quenching. Distortion, residual stress, average surface hardness and standard deviation of surface hardness are regarded as the optimization objectives. A new heat transfer coefficient model is presented, five distinct heat transfer coefficients are used at various regions of the model. The five heat transfer coefficients are regarded as the design variables, and four regressive equations are established by using response surface method. The four equations, respectively represent the relations between the four optimization objectives and the design variables. A multi-objectives optimization model is established, and the multi-objectives optimization model is optimized by the non-linear method. The optimized technology parameters are used to simulate the gas quenching process by FEM software. The quenching results after optimization are compared with those before optimization. The comparison shows that the quenching quality after optimization is better than that before optimization. After optimization, the four optimization objectives are all improved.     

An explicit solution to a tandem queueing model

We consider two queues in tandem, each with an exponential server, and with deterministic arrivals to the first queue. We obtain an explicit solution for the steady state distribution of the process (N₁(t), N₂(t), Y(t)), where N_j(t) is the queue length in the jth queue and Y(t) measures the time elapsed since the last arrival. Then we obtain the marginal distributions of (N₁(t), N₂(t)) and of N₂(t). We also evaluate the solution in various limiting cases, such as heavy traffic. This revised version was published online in June 2006 with corrections to the Cover Date.     

Hydrogeochemistry of the Purana formations of eastern Madhya Pradesh in India

The Raipur and Indravati series comprising the Purana formations of Chhattisgarh consist of conglomerates, orthoquartzites, sub-arkoses, shales, limestones and dolomites. The lithofacies in these have considerable lateral variations. Both Mahanadi and Indravati basins are saucer-shaped with centripetal dips; the arenaceous rocks along the fringes have dips up to 15°, while the younger rocks in the centre are almost horizontal. In carbonate rocks, karst is developed on a regional scale with sinkholes of higher topographic areas linked with resurgences of low relief areas. Groundwater in the above formations occurs generally under water table condition, but in karstic limestone also under confined condition. The chemical relationship of groundwater circulating in the various lithofacies are plotted in the trilinear diagrams after Piper. Groundwater within depths of 92m has carbonate hardness (Secondary alkalinity) exceeding 50 per cent with the chemical properties dominated by alkaline earths and weak acids. The cations and anions in water from similar lithofacies of Mahanadi and Indravati basins are distributed in the same field of the trilinear diagram with almost similar scatter of ions suggesting thereby a similar geochemical environment. The quality of groundwater is within permissible limits for irrigation and domestic purposes, while softening of water from temporary bicarbonate hardness may be necessary for certain specific industries. Expansion of groundwater recharge by increasing the ‘area of spreading’ of flood water of the Mahanadi basin and application of the technique in the Indravati basin will enrich the soils. Prevention of disposal of industrial wastes underground, especially in karstic regions will be a primary step in pollution control.     

<Emphasis Type="Bold">NP</Emphasis> -Hardness of Largest Contained and Smallest Containing Simplices for <Emphasis Type="Italic">V</Emphasis>- and <Emphasis Type="Italic">H</Emphasis>-Polytopes

   Abstract. The problem of finding a d -simplex of maximum volume in an arbitrary d -dimensional V -polytope, for arbitrary d , was shown by Gritzmann et al. [GKL] in 1995 to be NP-hard. They conjectured that the corresponding problem for H -polytopes is also NP-hard. This paper presents a unified way of proving the NP-hardness of both these problems. The approach also yields NP-hardness proofs for the problems of finding d -simplices of minimum volume containing d -dimensional V - or H -polytopes. The polytopes that play the key role in the hardness proofs are truncations of simplices. A construction is presented which associates a truncated simplex to a given directed graph, and the hardness results follow from the hardness of detecting whether a directed graph has a partition into directed triangles.     

NP -Hardness of Largest Contained and Smallest Containing Simplices for V - and H -Polytopes

Abstract. The problem of finding a d -simplex of maximum volume in an arbitrary d -dimensional V -polytope, for arbitrary d , was shown by Gritzmann et al. [GKL] in 1995 to be NP-hard. They conjectured that the corresponding problem for H -polytopes is also NP-hard. This paper presents a unified way of proving the NP-hardness of both these problems. The approach also yields NP-hardness proofs for the problems of finding d -simplices of minimum volume containing d -dimensional V - or H -polytopes. The polytopes that play the key role in the hardness proofs are truncations of simplices. A construction is presented which associates a truncated simplex to a given directed graph, and the hardness results follow from the hardness of detecting whether a directed graph has a partition into directed triangles.     

Strength vs. toughness optimization of microstructured composites

Aim of this paper is to present a new fractal approach linking the macroscopic mechanical properties of micro- and nano-structured materials with the main parameters: composition, grain size and structural dimension, as well as contiguity and mean free path. Assuming the key role played by the interfaces, the proposed fractal energy approach unifies the influences of all the above parameters, through the introduction of a fractal structural parameter (FSP), which represents an extension of the Gurland’s structural parameter. This modeling approach is assessed through an extensive comparison with experimental data on poly crystalline diamond (PCD) and WC–Co alloys. The results clearly show that the theoretical fractal predictions are in a fairly good agreement with the experiments on both hardness and toughness. This new synthetic parameter is thus proposed to investigate, design and optimize new micro- and nano-grained materials. Eventually, FSP-based optimization maps are developed, that allow to design new materials with high hardness and toughness.     

Invariant surfaces of the Heisenberg groups

Summary We fix a left-invariant metric g in the eisenberg group,H ₃, and give a complete classification of the constant mean curvature surfaces (including minimal) which are invariant with respect to 1-dimensional closed subgroups of the connected component of the isometry group of (H ₃, g). In addition to finding new examples, we organize in a common framework results that have appeared in various forms in the literature, by the systematic use of Riemannian transformation groups. Using the existence of a family of spherical surfaces for all values of nonzero mean curvature, we show that there are no complete graphs of constant mean curvature. We extend some of these results to the higher dimensional Heisenberg groupsH _2n+1. Entrata in Redazione il 2 aprile 1998. The first author was supported by Fapesp (Brazil), the second was partially supported by Fapesp and CNPq (Brazil), and the third was partially supported by Fapesp.