Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

N-Urethane-Protected Amino Alkyl Isothiocyanates: Synthesis, Isolation, Characterization, and Application to the Synthesis of Thioureidopeptides

Synthetically useful N-Fmoc amino-alkyl isothiocyanates have been described, starting from protected amino acids. These compounds have been synthesized in excellent yields by thiocarbonylation of the monoprotected 1,2-diamines with CS2/TEA/p-TsCl, isolated as stable solids, and completely characterized. The procedure has been extended to the synthesis of amino alkyl isothiocyanates from Boc- and Z-protected amino acids as well. The utility of these isothiocyanates for peptidomimetics synthesis has been demonstrated by employing them in the preparation of a series of dithioureidopeptide esters. Boc-Gly-OH and Boc-Phe-OH derived isothiocyanates 9a and 9c have been obtained as single crystals and their structures solved through X-ray diffraction. They belong to the orthorhombic crystal system, and have a single molecule in the asymmetric unit (Z′ = 1). 9a crystallizes in the centrosymmetric space group Pbca, while 9c crystallizes in the noncentrosymmetric space group P212121.

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.

Visualization of enantiomers using natural abundant 13C-filtered single and double quantum selective refocusing experiments: Application to small chiral molecules

The routine use of proton NMR for the visualization of enantiomers, aligned in the chiral liquid crystal solvent poly-γ-benzyl-l-glutamate (PBLG), is restricted due to severe loss of resolution arising from large number of pair wise interaction of nuclear spins. In the present study, we have designed two experimental techniques for their visualization utilizing the natural abundance 13C edited selective refocusing of single quantum (CH-SERF) and double quantum (CH-DQSERF) coherences. The methods achieve chiral discrimination and aid in the simultaneous determination of homonuclear couplings between active and passive spins and heteronuclear couplings between the excited protons and the participating 13C spin. The CH-SERF also overcomes the problem of overlap of central transitions of the methyl selective refocusing (SERF) experiment resulting in better chiral discrimination. Theoretical description of the evolution of magnetization in both the sequences has been discussed using polarization operator formalism.

Amide-based Room Temperature Molten Salt as Solvent cum Stabilizer for Metallic Nanochains

A simple and efficient method for spontaneous organization of long assemblies of gold nanoparticles is described. This is achieved in a molten solvent containing acetamide, urea and ammonium nitrate that acts as a solvent cum stabilizer. There is no external aggregating agent or stabilizing agent added to the system. Depending on the concentration of the metal salt in the ternary melt, either chain-like assemblies or individual nanoparticles could be obtained. The amine groups present in the components of the melt (acetamide and urea) help in the stabilization of nanoparticles. Ammonium ions present in the eutectic mixture are likely to assist in the organization of the particles. The method is simple, highly reproducible and does not require any templating agent for the formation of chain-like assemblies.

Molecular analysis of inorganic nitrogen assimilation in yeasts

Assimilation of nitrate and various other inorganic nitrogen compounds by different yeasts was investigated. Nitrate, nitrite, hydroxylamine, hydrazine, ammonium sulphate, urea and L-asparagine were tested as sole sources of nitrogen for the growth of Candida albicans, C. pelliculosa, Debaryomyces hansenii, Saccharomyces cerevisiae, C. tropicalis, and C. utilis. Ammonium sulphate and L-asparagine supported the growth of all the yeasts tested except D. hansenii while hydroxylamine and hydrazine failed to support the growth of any. Nitrate and nitrite were assimilated only by C. utilis. Nitrate utilization by C. utilis was also accompanied by the enzymatic activities of NAD(P)H: nitrate oxidoreductase (EC 1.6.6.2) and NAD(P)H: nitrite oxidoreductase (EC 1.6.6.4), but not reduced methyl viologen-or FAD-nitrate oxidoreductases (EC 1.7.99.4). It is demonstrated here that nitrate and nitrite reductase activities are responsible for the ability of C. utilis to assimilate primary nitrogen.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Growth requirements of some fungi causing maduromycosis

Three strains ofMadurella mycetomi, two ofM. grisea, and two ofRhinocladiella mansonii have been studied for ossible differences in growth requirements which might be used for distinguishing these species. Under the experimental conditions, an incubation temperature of 37C suitedM. mycetomi about as well as 30C.R. mansonii grew less well at 37C than at 30C, andM. grisea did not grow at the higher temperature. M. grisea andR. mansonii further differed fromM. mycetomi in that they required thiamine for growth. The pH tolerance of all the strains was very wide. Asparagine and potassium nitrate were readily utilized by all the strains, but ammonium salts were not. Urea was poorly used byM. mycetomi; the other species did not use it. A possible relationship ofM. grisea andR. mansonii is discusse

Studies on nucleotidases in plants : Reversible denaturation of the crystalline mung bean nucleotide pyrophosphatase and the effect of adenylates on the native and renatured enzyme

The crystalline mung bean nucleotide pyrophosphatase was inhibited nonlinearly by AMP, one of the products of the reaction. The partially inactive enzyme was specifically reactivated by ADP, and V at maximal activation was the same as that of the native enzyme. ATP was a linear, noncompetitive inhibitor. The kinetic evidence suggested that ADP and ATP might not be reacting at the same site as AMP. The electrophoretic mobility of the enzyme was increased by AMP, whereas ADP and ATP were without effect. The enzyme was denatured on treatment with urea or guanidine hydrochloride. The renatured and the native enzyme had the same pH (9.4) and temperature (49 °C) optimum. The Km (0.2 mImage ) and V (3.2) of the native enzyme increased on renaturation to 1.8 mImage and 8.0, respectively. In addition, renaturation resulted in desensitization of the enzyme to inhibition by low concentrations of AMP. Renaturation did not affect the reactivation of the apoenzyme by Zn2+.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Immunologic studies on nucleic acids and their components II. Reversible inhibition of anti-nucleoside antibodies in aqueous pyridine and its application in antibody

The effect of aqueous pyridine on a hapten—antihapten system was investigated by the quantitative precipitin reaction and by the membrane filtration method. It was found that dilute solutions of pyridine inhibited the reaction between isopentenyladenosine and its antiserum. Other solvents examined were less effective. The effect of pyridine was reversible at concentrations where complete inhibition occurred, thus indicating its use for the dissociation of antigen—antibody complexes. The inhibitory effect of pyridine was exploited in a single-step purification method for anti—isopentenyladenosine and antideoxy-adenylate antibodies. In addition, generally applicable methods for linking nucleosides and nucleotides to aminoethyl-Sepharose are described.

Studies on nucleotidases in plants - Reversible denaturation of the crystalline mung bean nucleotide pyrophosphatase and the effect of adenylates on the native and renatured enzyme

The crystalline mung bean nucleotide pyrophosphatase was inhibited nonlinearly by AMP, one of the products of the reaction. The partially inactive enzyme was specifically reactivated by ADP, and V at maximal activation was the same as that of the native enzyme. ATP was a linear, noncompetitive inhibitor. The kinetic evidence suggested that ADP and ATP might not be reacting at the same site as AMP. The electrophoretic mobility of the enzyme was increased by AMP, whereas ADP and ATP were without effect. The enzyme was denatured on treatment with urea or guanidine hydrochloride. The renatured and the native enzyme had the same pH (9.4) and temperature (49 °C) optimum. The Km (0.2 m ) and V (3.2) of the native enzyme increased on renaturation to 1.8 m and 8.0, respectively. In addition, renaturation resulted in desensitization of the enzyme to inhibition by low concentrations of AMP. Renaturation did not affect the reactivation of the apoenzyme by Zn2+.

A note on the application of a radiation condition for a source in a rotating stratified fluid

The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.