Lower bounds for linear forms

Discriminating cyclic from linear nucleotides − CRISPR/Cas-related cyclic hexaadenosine monophosphate as a case study

Aim/purpose – Shelf space is one of the most important tools for attracting customers’ attention in a retail store. This paper aims to develop a practical shelf space allocation model with visible vertical and horizontal categories. and formulate it in linear and non- -linear forms. Design/methodology/approach – The research is mainly based on operational research. Simulation, mathematical optimization, and linear and nonlinear programming methods are mainly used. Special attention is given to the decision variables and constraints. Changing the dimensioning of the decision variables results in an improvement in the formulation of the problem, which in turn allows for obtaining an optimal solution. Findings – A comparison of the developed shelf space allocation models with visible vertical and horizontal categories in linear and nonlinear forms is presented. The compu- tational experiments were performed with the help of CPLEX solver, which shows that the optimal solution of the linear problem formulation was obtained within a couple of seconds. However, a nonlinear form of this problem found the optimal solution only in 19 out of 45 instances. An increase in the time limits slightly improves the performance of the solutions of the nonlinear form. Research implications/limitations – The main implication of research results for sci- ence is related to the possibility of determining an optimal solution to the initially formu- lated nonlinear shelf space allocation problem. The main implication for practice is to take into consideration the practical constraints based on customers’ requirements. The main limitations are the lack of storage conditions and holding time constraints. Originality/value/contribution – The main contribution is related to developing math- ematical models that consider simultaneous categorization of products vertically, based on one characteristic, and horizontally, based on another characteristic. Contribution is also related to extending the shelf space allocation theory with the shelf space allocation problem model in relation to four sets of constraints: shelf constraints, product con- straints, orientation constraints, and band constraints. Keywords: Retailing, decision making/process, merchandising, shelf space allocation, planogram. JEL Classification: C61, L81.

In this chapter, we continue our study of Banach and Hilbert spaces. Here, we mainly consider linear functionals, i.e., additive, homogeneous, and continuous number functions given on such spaces. The problems under consideration are mostly grouped around two fundamental facts, namely, the Hahn-Banach theorem on extensions of linear functionals and the Banach-Steinhaus theorem (the principle of uniform boundedness). The general form of linear continuous functionals in many important spaces and some geometric problems in the theory of Hilbert spaces are also investigated.

Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data

It is shown that the ordinary Schrodinger equation for a dynamical system gs may be replaced by a more general equation, which has the form of the Schrodinger equation of a quantized Bose field whose quanta are the systems gs. The linear wave functionals of the quantized field describe pure states of the system gs and the non linear wave functionals describe, in general, mixtures of states of gs. The representation in which the emission operators of the quantized gs field are diagonal plays a central role in the present formalism. It is shown that the eigenfunctionals of the absorption operators of the quantized gs field can be used to obtain a new description of the states of a system gs, the expectation values of the field quantities in suitably chosen eigenstates of the emission operators coinciding with the expectation values of the corresponding quantities in the pure states of gs, but the fluctuations being larger in the former case. The eigenfunctionals of the absorption operators have the remarkable property of being matrix elements of the unity operator of the field formalism, and seem to be of a more fun damental nature than the linear functionals which correspond to the ordinary description of the pure states by means of the wave functions of gs.

The purpose of this study is to explain the changes and inheritance of PAN vowels into Javanese (BJ) and Minangkabau (BM) languages. The approach used is the Comparative Historical Linguistics (LHK) approach. The data used is 200 swadesh vocabulary lists. The method used for data analysis is comparative historical method. The results of this study indicate that the inheritance of vowel phonemes in Javanese and Minangkabau languages ​​occurs in linear forms and innovative forms. Linear forms in Javanese are found in vowel phonemes /*a/, /*i/, /*e/, /*ə/ and /*u/ and innovative forms in Javanese are found on the vowel phonemes /*a/, /*i/, /*u/. the changes in vocal phonemes that occur in the innovative form occur in vocal phonemes /*a/ which change into vowel phonemes /o/, /ə/, and /e/. The vowel phoneme /*i/ changes to the vowel phoneme /e/ and the vowel phoneme /*u/ changes to the vowel phoneme /o/. For vowel phoneme forms in the Minangkabau language it is also found in linear and innovative forms where in vowel phonemes the linear form is found in the vowels /*a/, /*i/ and /*u/. In the innovative form it is found in the vowel phonemes /*a/, /*ə/, /*u/ where the vocal phonemes /*a/ and the vowel phonemes /*ə/ and /*u/. The changes in vocal phonemes that occur are the vocal phoneme /*a/ which changes to the vocal phoneme /o/, the vocal phoneme /*ə/ changes to the vocal phoneme /a/, and the vocal phoneme /*u/ changes to the vocal phoneme /o/.

This research of the relationship of firms’ financial leverage with firms’ performance is based on six year (2008-2013) financial record of 151 textile companies. The net profit before tax (NPBT) has been used as proxy to represent the firm profitability while total debt as a ratio of total equity has been defined as financial leverage. Of the total, 17 firms (11%) have been found with negative NPBTs, 36 firms (24%) have positive NPBTs and 98 firms (65%) have mix NPBTs (having positive for some years and negative for some years). The trend analysis suggests that on average financial leverage of negative NPBT yielding firms remained at -28.756 and increased by 2.747 every year during the period of 2008 to 2013. While the average leverage of mixed NPBT yielding firms remained positive at 1.939 and increased by 0.174 every year, and the average leverage of positive NPBT yielding firms remained at 1.547 and decreased by 0.007 every year during the studied period (2008-13). Leaving negative NPBT yielding firms aside, the average leverage of mixed NPBT yielding firms is higher (1.939) and has been being increased (0.174 per year) while that of positive NPBT yielding firms is relatively lower (1.547) and has decreased (0.007 per year). Separating all negative equity and negative NPBT bearing observations, we are left with 519 positive equity positive NPBT yielding observations. The mean value of leverage (L) of these observations is estimated at 1.8338 and ranged between a minimum and maximum of 0.03 and 9.65. The mean value of NPTA (NPTA = NPBT/Total Assets) estimates at 0.0725 and ranges between minimum and maximum values of 0.0001 and 0.3233. For measuring a mathematical relationship between NPTA and L, the former variable was regressed over the latter, using three formulations (Linear form: NPTA = β0 β1L; Quadratic form: NPTA = β0 β1L β1L2; Cubic form: NPTA = β0 β1L β1L2 β1L3). The linear and squared form of the model gave good results; the cubic model yielded insignificant results. The results in the linear form (NPTA = 0.102 – 0.016L) suggest that there is an inverse relationship between leverage and profitability; for every one unit of leverage (L) increase, profitability (NPTA) decreases by 0.016 units. The results of the Quadratic form are reproduced, as follows: NPTA = 0.122 – 0.036L 0.003L2. Taking the F.O.C, and solving for L helps us estimate L = 6. These results suggest that with L = 0, the NPTA estimates at 0.122 (net profits are 12.20% of total assets) and with L = 6, NPTA minimizes at 0.014 (net profits drops to 1.40%). The existence of statistically significant inverse relationship between firms’ profitability and financial leverage persuades one to recommend that financial leverage be kept and managed as low as possible for greater firms’ profitability.

Aplication of the statistical experimental design to optimize mine-impacted water (MIW) remediation using shrimp-shell

Studies of the feasibility of a subunit vaccine to protect against human immunodeficiency virus (HIV) infection have principally focused on the third variable (V3) loop. The principal neutralizing determinant (PND) of HIV-1 is located inside the V3 loop of the surface envelope glycoprotein, gp120. However, progress toward a PND-based vaccine has been impeded by the amino acid sequence variability in the V3 loops of different HIV isolates. Theoretical studies revealed that the variability in sequence and structure of the V3 loop is confined to the N- and C-terminal sides of the conserved GPG crest. This leaves three regions of the V3 loop conserved both in sequence and secondary structure. We present the results of NMR studies that test the validity of our theoretical predictions. Structural studies are reported for the HIV-V3 loop (HIV-MN) in the linear and cyclic (S-S-bridged) forms. For the V3 loop sequence of the HIV-MN isolate, the three conserved secondary structural elements are as underlined below: turns turn helix CTRPNYNKRKRIHIGPGRAFYTTKNIIGTIROAHC Finally, the conformational requirement of the PND in the V3 loop-antibody interaction is tested by monitoring the monoclonal antibody binding to the HIV-MN V3 loop in the linear and cyclic forms by enzyme-linked immunosorbent assay. The binding data reveal that the cyclic V3 loop is a better ligand for the monoclonal antibodies than the linear form although the latter has the same sequence. This means that the monoclonal antibodies recognize the PNDs as conformational epitopes.

Owing to various anthropogenic activities our environment is being polluted especially by discharging effluents containing heavy metals. Heavy metals are non degradable and persist for a long time in the environment. Hence they pose potential risk on the environment. Cadmium is a toxic element and cause severe damages to both animals and plants. Biosorption which is a process that utilizes dead or living biomass to sequester heavy metals is currently gaining considerable important as an alternative low cost and eco-friendly technology to remove heavy metals from aquatic media. In this study, three aquatic plants such as Eichhornia crassipes, Ceratophyllum demersum and Salvinia mullets were screened for the biosorption of cadmium and the plant biomass was analyzed for Cd using Atomic Absorption Spectrometer. Ceratophyllum demersum was selected and batch experiments were carried out to examine the influence of biosorbent dosage, initial concentration of metal ion and contact time on the cadmium (II) ion adsorption. Sorption data was analyzed using linear and nonlinear regression methods of Langmuir and Freundlich isotherm models. Desorption experiment was also carried out. Biosorption of cadmium by Ceratophyllum demersum was very rapid (20 minutes) at pH 5 and at room temperature. Adsorption capacity of Ceratophyllum demersum for cadmium increased with increasing concentration of Cd ions. The nonlinear adsorption isotherm of Langmuir model did not fit well with the sorption data (high χ2 = 4.58). Although three linear forms (I, II and V) of Langmuir isotherm model supported the sorption data (R2=0.9316, 0.9124 and 0.912), however the separation factor, RL, was less than zero and also maximum adsorption capacity, qm were very low in all five linear forms. Both linear and nonlinear forms of Freundlich adsorption isotherm model exhibited a better fit with high correlation R2=0.92 and low χ2 = 1.95 respectively, which indicates a multilayer adsorption. Desorption experiments indicated that 0.1M EDTA, 0.1M HCl and 0.1M HNO3 were efficient desorbents for recovery of Cd (II) from the loaded biomass. Journal of Environmental Professionals Sri Lanka: 2015 Vol. 4 No. 2: 10-24

Properties of prey sensory systems are important factors shaping the design of signals generated by organisms exploiting them. In this study we assessed how prey sensory preference affected the exploiter signal design by investigating the evolutionary relationship and relative attractiveness of linear and cruciate form web decorations built by Argiope spiders. Because insects have an innate preference for bilaterally symmetrical patterns, we hypothesized that cruciate form decorations were evolved from linear form due to their higher visual attractiveness to insects. We first reconstructed a molecular phylogeny of the Asian members of the genus Argiope using mitochondrial markers to infer the evolutionary relationship of two decoration forms. Results of ancestral character state reconstruction showed that the linear form was ancestral and the cruciate form derived. To evaluate the luring effectiveness of two decoration forms, we performed field experiments in which the number and orientation of decoration bands were manipulated. Decoration bands arranged in a cruciate form were significantly more attractive to insects than those arranged in a linear form, no matter whether they were composed of silks or dummies. Moreover, dummy decoration bands arranged in a cruciate form attracted significantly more insects than those arranged in a vertical/horizontal form. Such results suggest that pollinator insects' innate preference for certain bilateral or radial symmetrical patterns might be one of the driving forces shaping the arrangement pattern of spider web decorations.

Comparison of the nonlinear and linear forms of the van't Hoff equation for calculation of adsorption thermodynamic parameters (∆S° and ∆H°)

Investigating the effects of ingredient levels on physical quality properties of cooked hamburger patties using response surface methodology and image processing technology

This study aims to purify water from hazardous dyes and for this purpose, a novel adsorbent is developed that was synthesized by using sodium alginate, guar gum and iron coated activated alumina (SA@GG@ICAA Composites) with the Ion Gelation Method. The novel composites were characterized by using SEM, XRD, DSC, FTIR, BET, EDX, zeta potential and zeta sizer. These novel composites were used for the removal of Direct Blue 86 (DB86). The surface area of the adsorbent was found to be 5.606 m2/g. Zeta size and zeta potential was found to be 169.9 nm and −47.7 mV, respectively. Optimized parameters were achieved for best adsorption of the selected dye. For DB86, the removal efficiency was found to be 97% at 40 ppm (dye concentration), 150 min (contact time), 3 (pH) and 150 mg (adsorbent concentration) at λmax of 620 nm. Linear and non-linear forms of adsorption isotherms are applied on the experimental data to check the adsorption methodology and its chemistry. The non-linear form of the Freundlich isotherm was found to be best fitted for the current work (0.942) as compared with the linear form (0.76). The first order kinetics model and second order kinetics model are applied in both linear and non-linear forms, and results with a high R2 value were obtained for the non-linear form of pseudo-first order kinetics. The adsorption mechanism was found to be electrostatic based on the interaction of the adsorbent and dye. Synthesized adsorbent can be successfully applied for the removal of DB86 dye from waste water.

The numerical analysis of statistical properties linear binary forms of currency tools quotations is carried out. Variants of construction of the specified linear forms for 25 criteria of their selection are resulted. Selection rules correspond to a choice of linear forms with the statistical characteristics defining the trading strategy technologies. Presence of relative time stability of the ratings is established. This is allowing to use results of selection directly at trading operations carrying out or to correct them on the basis of the adaptive approach.