Generic Formulae Research Articles

New More Generic and Inclusive Regression Formulae for the Estimation of Stature from Long Bone Lengths in Children

Existing child stature estimation methods have a number of disadvantages. This paper addresses some of these limitations by developing regression-based stature estimation formulae that are more generic and inclusive. A sample of 142 individuals under 12 years of age from the Hamann—Todd Human Osteological Collection and the New Mexico Decedent Images Database were used to generate five least squares linear regression formulae to estimate stature from the diaphyseal length of long bones. All models showed excellent fits to the data (R2 close to or at 0.98), and internal validation confirmed the stability and accuracy of model parameters. External validation was performed using a sample of 14 individuals from the Lisbon Collection and the Victoria Institute of Forensic Medicine. Overall, the humerus provides the most accurate estimate of stature, but the femur and tibia showed the greatest coverage. These formulae can be used in a variety of contexts and are not dependent on group affiliation, including sex.

An Application of BP Neural Network to the Prediction of Compressive Strength in Circular Concrete Columns Confined with CFRP

The neural network comprises many neurons with extensive interconnections operating parallel and performing specific functions. This paper establishes a BP neural network prediction model for the compressive strength of CFRP-confined concrete based on a large number of experimental data to study the predictive ability of the BP neural network on the compressive strength of CFRP-confined concrete and the output performance of the neural network model. The model is based on a BP neural network that has been trained using many experimental data. An investigation is being conducted on the effect of different data combinations on the accuracy of the predictions made by the neural network model. The high-precision BP network model is created into generic and simplified formulae for application convenience. These formulas are developed based on the theory of neural networks. The neural network models' findings and the empirical formulae for making predictions are compared and discussed. The BP neural network accurately predicts the compressive strength of CFRP-confined concrete, with over 90% of its data points having less than 15% error. In comparison, the regression model shows less accuracy, with less than 70% of its data points having an error within 15%. Compared to traditional regression models, the simple linear equation derived using Purelin instead of Sigmoid as the transfer function only adds a constant term. The average value of prediction/test results is 1.011. The analysis results show that BP neural network can extract the input and output parameters' data information well and obtain a high-accuracy prediction model. The coefficient of variation is 0.112, which indicates that the prediction accuracy and stability are greater than average.

Algorithm for Combinatorial Bipartite Enumeration of Chiral and Achiral Stereoisomers of Homo- and Heteropolysubstituted Derivatives of the Cubane Molecule

This paper is devoted to the application of an algorithm for the enumeration of chiral and achiral stereoisomers of homo and heteropolysubstituted derivatives of the cubane molecule. The sequence of this algorithm is in three steps, the first of which is the determination of the permutations of 8 hydrogen atoms of the cuban molecule ( ) subjected to the action of the Oh group. The second step will be the composition of these permutations later into permutational representations and controlling respectively the chirality and achirality of this molecular system. The transformation of these 2 operators into a pair of generic formulae used for bipartite combinatorial enumeration giving chiral and achiral isomer numbers of the homo- and hetero-polysubstituted derivatives of the cubane molecule respectively symbolised by the empirical formulae and being the final step.

Thermo-dielectric, humidito-dielectric, and humidity sensing properties of barium monoferrite and barium hexaferrite nanoparticles

Barium monoferrite and M−type hexaferrite with generic formulae BaFe2O4 and BaFe12O19 were synthesized using the sol–gel method by annealing at 1000 °C. To confirm the phase and compositions, XRD and FTIR analyses were employed, and the formation of orthorhombic crystal structure of BaFe2O4 and hexagonal crystal structure of BaFe12O19 were observed. The surface morphology of the samples was investigated through the use of the scanning electron micrograph (SEM) technique. Energy dispersive X-ray spectroscopy (EDS) confirmed the chemical compositions of the samples. At room temperature, the real part of the dielectric constant (ɛʹ), the imaginary part of the dielectric constant (ɛʹʹ), the dielectric loss tangent (tanδ), and AC conductivity (σAC) were measured at the specific frequencies (1, 1.5, and 2 MHz), and they were increased with both temperature and relative humidity (RH). Barium ferrite humidity sensors were created. The resistance of the sensor goes down as the RH% goes up, and the BaFe12O19 humidity sensor is 1.82 times more sensitive than the BaFe2O4 sensor.

On the Courant–Friedrichs–Lewy condition for numerical solvers of the coagulation equation

ABSTRACTEvolving the size distribution of solid aggregates challenges simulations of young stellar objects. Among other difficulties, generic formulae for stability conditions of explicit solvers provide severe constraints when integrating the coagulation equation for astrophysical objects. Recent numerical experiments have reported that these generic conditions may be much too stringent. By analysing the coagulation equation in the Laplace space, we explain why this is indeed the case and provide a novel stability condition that avoids time oversampling.

A method to choose water depths for zooplankton samples in lakes

AbstractAs methods in the literature to sample zooplankton in lakes mostly offered general guidance on the sample depths, a new one was developed. Using the principle of volume‐weighted sampling of the lake volume and an empirical function for the hypsometric curve, formulae for the volumes and areas of five equal sections of the lake were derived, which were then used to calculate section mean depths. Vertical net hauls taken at the mean depths are combined using a relation between their mean depths to produce one unbiased composite sample of the zooplankton. While generic formulae were derived, starting values for the depths that divide the lake volume into five equal sections are needed in order to apply the method, which then optimizes the depths; the method is implemented in a spreadsheet. The method was applied to four hypothetical lakes of maximum depth 12 m that cover a wide variation of lake form and how the sample depths vary with form was described; as lake form becomes more convex, the sample depths decrease, reflecting that more of the lake volume is at shallower depth. The method was used to estimate the whole‐lake abundance of zooplankton in 51 lakes and no practical difficulties were encountered. It can be used in lakes up to a few tens of km2 in area.

Model independent analysis of Dirac CP violating phase for some well-known mixing scenarios

In this paper, we present a model independent analysis of Leptonic CP violation for some well-known mixing scenarios. In particular, we considered modified schemes for bimaximal (BM), democratic (DC), hexagonal (HG) and tribimaximal (TBM) mixing for our numerical investigation. These model independent corrections to mixing matrices are parametrized in terms of complex rotation matrices [Formula: see text] with related modified PMNS matrix of the forms [Formula: see text] where [Formula: see text] is a complex rotation in [Formula: see text] sector and [Formula: see text] is unperturbed mixing scheme. We present generic formulae for mixing angles, Dirac CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] in terms of correction parameters. The parameter space of each modified mixing case is scanned for fitting neutrino mixing angles using [Formula: see text] approach and the corresponding predictions for Leptonic CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] has been evaluated from allowed parameter space. The obtained ranges are reported for all viable cases.

Dark nucleosynthesis: cross-sections and astrophysical signals

We investigate dark matter bound-state formation and its implication for indirect-detection experiments. We focus on the case where dark matter is a baryon of a strongly-coupled dark sector and provide generic formulae for the formation of shallow nuclear bound states on emission of photons, and W and Z gauge bosons. These processes can occur via electric and magnetic transitions, and give rise to indirect signals that are testable in monochromatic and diffuse photon measurements by Fermi and HESS. We also study the validity of factorizing the bound-state formation cross section into a short-distance nuclear part multiplied by Sommerfeld-enhancement factors. We find that the short-distance nuclear potential often violates factorization, modifying in particular the location of the peaks associated with zero-energy bound states. Finally we revisit bound-state formation of a (weakly-coupled) Minimal DM quintuplet including isospin-breaking effects, and find it gives rise to indirect-detection signals that are compatible with current bounds.

Influence of Gd/Nb on activation energy, relaxation response, impedance, Nyquist plots and dielectric studies at high frequency of BaTiO3-Li0.5Fe2.5O4 solid compounds

The Gd/Nb doped ferroelectric- ferrite solid composite having a generic formulae (0.9)BaTi (1-2x) GdxNbxO3 – (0.1)Li0.5Fe2.5O4 (x = 0, 0.05 and 0.1) synthesized using a normal solid state method. The frequency dependent of impedance spectroscopic studies at different temperatures, relaxation time with temperature, estimate the activation energy, Nyquist plots, the high frequency dielectric permitivity (ε′) and dielectric dissipation at 30 °C have been observed. The real impedance (Z′) peaks of all samples are merging in the high frequency region at all temperatures represent a feasibility of liberation of space charge polarization in the samples. As and when an increase in temperature, the maximum impedance Z′′max peak moved towards higher frequency. The relaxation time (τ) of all composites decrease steeply with increase temperature. The activation energy of BLF reduces as when Gd/Nb doped in BLF which indicates change in degree of freedom of dipoles to orient itself in the applied field direction. In Nyquist plots, all composites exhibit single semicircle at all temperatures, which represents the Debye type of relaxation exist in the composites. The dielectric permitivity (ε′) of all composites decreases steeply up to 1 GHz frequency beyond that its exhibits as complex behavior. The dielectric dissipation of all the samples exhibit jumping behavior due to Debye relaxation at high frequency region.

New minimal supersymmetric GUT emergence and sub-Planckian renormalization group flow

Consistency of trans-unification renormalization group (RG) evolution is used to discuss the domain of definition of the New Minimal Supersymmetric SO(10)GUT (NMSGUT). We define the 1-loop RGE $\ensuremath{\beta}$ functions, simplifying generic formulae using constraints of gauge invariance and superpotential structure. We also calculate the 2 loop contributions to the gauge coupling and gaugino mass and indicate how to get full 2 loop results for all couplings. Our method overcomes combinatorial barriers that frustrate computer algebra based attempts to calculate SO(10) $\ensuremath{\beta}$ functions involving large irreps. Use of the RGEs identifies a perturbative domain $Q<{M}_{E}$, where ${M}_{E}<{M}_{\text{Planck}}$ is the scale of emergence where the NMSGUT, with GUT compatible soft supersymmetry breaking terms emerges from the strong UV dynamics associated with the Landau poles in gauge and Yukawa couplings. Due to the strength of the RG flows the Landau poles for gauge and Yukawa couplings lie near a cutoff scale ${\mathrm{\ensuremath{\Lambda}}}_{E}$ for the perturbative dynamics of the NMSGUT which just above ${M}_{E}$. SO(10) RG flows into the IR are shown to facilitate small gaugino masses and generation of negative Non Universal Higgs masses squared needed by realistic NMSGUT fits of low energy data. Running the simple canonical theory emergent at ${M}_{E}$ through ${M}_{X}$ down to the electroweak scale enables tests of candidate scenarios such as supergravity based NMSGUT with canonical kinetic terms and NMSGUT based dynamical Yukawa unification.

Polarizability of isomeric and related interstellar compounds in the aspect of their abundance

Currently, about 100 carbon-containing molecules have been detected in interstellar and circumstellar environments, and this list includes isomeric substances. In most cases, the minimum energy principle is able to explain the ratio of abundances of the isomeric compounds but in some cases is not. Trying to rationalize the questions unsolved within the energetic approach, we have theoretically studied the polarizability of isomeric and related compounds detected or proposed in interstellar conditions. As we found, in general both energy and polarizability provide the consistent estimates for the ratio of the isomers (e.g., for the isomers having generic formulae CHO, CHN, C3H, C3H2, CHNO, C2H3N, C2H6O, etc.). In the case of the C4H3N isomers, the most abundant isomer (cyanoallene) is not the most stable but the least polarizable that is in a good agreement with relevant experimental study. We assume that the efficiency of the use of polarizability is due to its relevance to the molecules’ response to the external electric fields, i.e., more polarizable molecules are more responsive, more reactive, and, hence, less abundant. Further, we have analyzed the polarizabilities of polycyclic aromatic hydrocarbons, fullerene hydrides (fulleranes), polyynes, and their derivatives with respect to their possible detection under interstellar conditions.

Complexes of Stiboranium Mono-, Di-, and Trications.

Reaction of Ph2 SbCl3 with 2,2'-bipyridine and Me3 SiOSO2 CF3 releases chlorobenzene, which is interpreted as a reductive (SbV /SbIII ) elimination from a complex of a stiboranium cation. Conversely, reactions of Ph2 SbCl3 with 4-methylpyridine-N-oxide and AgOSO2 CF3 give redox-resistant complexes with the generic formulae [Ph2 SbCl3-x Lx+1 ][OTf]x , including a compound containing a pnictogen(V) trication.

Settling velocity of quasi-neutrally-buoyant inertial particles

We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady) flows, along with further information for flows endowed with some degree of spatial symmetry such as odd parity in the vertical direction. These expressions consist in space-time integrals of auxiliary quantities that satisfy partial differential equations of the advection–diffusion–reaction type, which can be solved at least numerically, since our scheme implies a huge reduction of the problem dimensionality from the full phase space to the classical physical space.

The maximum sizes of large scale structures in alternative theories of gravity

The maximum size of a cosmic structure is given by the maximum turnaround radius—the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum turnaround radius in any theory of gravity obeying the Einstein equivalence principle, in two situations: on a spherically symmetric spacetime and on a perturbed Friedman-Robertson-Walker spacetime. We show that the two formulae agree. As an application of our formula, we calculate the maximum turnaround radius in the case of the Brans-Dicke theory of gravity. We find that for this theory, such maximum sizes always lie above the ΛCDM value, by a factor 1 + 1/3ω, where ω≫ 1 is the Brans-Dicke parameter, implying consistency of the theory with current data.

On the Loewy length of the center of a block with elementary abelian defect groups

ABSTRACTLet G be a finite group and k an algebraically closed field of characteristic p. In this paper we investigate the Loewy structure of centers of indecomposable group algebras kG, for groups G with a normal elementary abelian Sylow p-subgroup. Furthermore, we show a reduction result for the case that a normal abelian Sylow p-subgroup is acted upon by a subgroup of its automorphism group; this is fundamental in providing generic formulae for the Loewy lengths considered.

Time-delay and reality conditions for complex solitons

We compute lateral displacements and time-delays for scattering processes of complex multi-soliton solutions of the Korteweg de-Vries equation. The resulting expressions are employed to explain the precise distinction between solutions obtained from different techniques, Hirota’s direct method and a superposition principle based on Bäcklund transformations. Moreover they explain the internal structures of degenerate compound multi-solitons previously constructed. Their individual one-soliton constituents are time-delayed when scattered amongst each other. We present generic formulae for these time-dependent displacements. By recalling Gardner’s transformation method for conserved charges, we argue that the structure of the asymptotic behaviour resulting from the integrability of the model together with its PT-symmetry ensures the reality of all of these charges, including in particular the mass, the momentum, and the energy.

Making and Unmaking ‘African Foreignness’: African Settings, African Migrants and the Migrant Detective in Contemporary South African Crime Fiction

This article aims to examine the portrayal of African migrants and South Africa’s relationship to the African continent in post-apartheid crime fiction. Exotic settings and the figure of the stranger have featured in the crime genre since its emergence in the 19th century. Reading Mike Nicol’s The Ibis Tapestry (1998), his trilogy Payback (2008), Killer Country (2010) and Black Heart (2011), and H.J. Golakai’s novel The Lazarus Effect (2011), this article suggests that the themes of migration and ‘xenophobia’ have become central to reconfigured socio-political commitment in contemporary South African crime fiction. The article argues that the re-writing of generic formulae and boundaries in The Ibis Tapestry and The Lazarus Effect becomes a powerful vehicle for an enquiry into constructions of ‘foreignness’ and a means to allot a space to African migrants in the ‘new’ South African imaginary. The simultaneous unmaking and remaking of ‘African foreignness’ that characterizes the Revenge trilogy draws attention to the paradoxical temporality of transitional literatures and cultural formations, in which former discourses of ‘the foreign’ remain imprinted.

An improved method for pricing and hedging long dated American options

The majority of quasi-analytic pricing methods for American options are efficient near maturity but are prone to larger errors when time-to-maturity increases. We introduce a new methodology to increase the accuracy of almost any existing quasi-analytic approach in pricing long-maturity American options. The new methodology, called the “extension-method”, relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches so that the maturity range for which small errors are attainable is extended. Our method retains the quasi-analytic nature of the methods it improves. Generic quasi-analytic formulae for the price of an American put as well as for its hedging parameter are derived. Our scenarios-based numerical study indicates that our method considerably improves both the pricing and the hedging performance of a number of established approaches for a wide range of maturities. The superiority of this approach is illustrated with real financial data by considering S&P 100TM LEAPS® options traded from January 2008 to May 2015.

Complexes of trimethylsilyl trifluoromethanesulfonate with nitrogen, oxygen, and phosphorus donors

The Lewis acceptor chemistry of Me3SiOTf with p-block Lewis bases has been explored and a library of complexes has been characterized by spectroscopic and, where possible, crystallographic methods. Compounds with the generic formula [Me3Si(L)][OTf] (L = 4-dmap, pyr, imz, OPMe3, OPCy3, OPPh3, OpyrMe, dmso, PMe3) were isolated from 1:1 mixtures of Me3SiOTf and the respective ligand in CH2Cl2. Characterization by NMR spectroscopy confirmed the solution stability of all but [Me3Si(PMe3)][OTf], with indications that the latter dissociates into PMe3 and Me3SiOTf. Solid-state structures of [Me3Si(4-dmap)][OTf], [Me3Si(pyr)][OTf], [Me3Si(OPCy3)][OTf], [Me3Si(OPPh3)][OTf], [Me3Si(OpyrMe)][OTf], and [Me3Si(PMe3)][OTf] were elucidated by single crystal X-ray diffraction, confirming the envisaged ionic formulations resulting from the displacement of the OTf anion from the silicon center of Me3SiOTf by the incoming ligand. Mixtures of Me3SiOTf with other related donors, including ChPPh3 (Ch = S or Se), NEt3, SMe2, PPh3, 2,2′-bipy, or Me2CO, show no evidence of reaction under ambient conditions, reflecting the lower basicity and (or) greater steric encumbrance of these ligands. Reactions of Me3SiOTf with bis-donor ligands yielded complexes of the generic formulae [Me3Si(L–L)SiMe3][OTf]2 (L–L = 4,4′-bipy, tmeda, dmpe) and [Me3Si(L–L)][OTf] (L–L = 4,4′-bipy, tmeda, dmpe). The tmeda and dmpe complexes, however, were found to dissociate in solution, with complexes only prevailing in the solid phase. X-ray diffraction studies of [Me3Si(4,4′-bipy)SiMe3][OTf]2 and [Me3Si(dmpe)SiMe3][OTf]2 confirmed the expected connectivities and ionic formulations, with Si–ligand bond lengths comparable to those observed in [Me3Si(pyr)][OTf] and [Me3Si(PMe3)][OTf], respectively.

Diabetes and oral therapies

Abstract For decades, antihyperglycaemic agents have been used for the treatment of type 2 diabetes mellitus given their effectiveness and convenience. Metformin (MET) and sulphonylureas (SU) are time-tested antihyperglycaemic agents that have been administered for more than 50 years. These agents were followed by the introduction of other antihyperglycaemic agents such as glinides (GLN), thiazolidinediones (TZD), alpha-glucosidase inhibitors (AGI), dipeptidyl peptidase-4 inhibitors (DPP-4I), and sodium–glucose cotransporter-2 inhibitors (SGLT2I). MET is recognized as the drug of choice for monotherapy unless contraindicated or unwanted side effects occur. SU-induced hypoglycaemia is losing ground to various new agents, but the generic formulae of SU together with MET are cheap and effective. The cardiovascular hazards of several agents are a major concern to physicians and legislating bodies. In choosing antihyperglycaemic agents for dual or triple therapy, the treating physician must keep in mind the health status of the patient, medication side effects, cost, and patient preference. This review addresses the advantages and disadvantages of a range of antihyperglycaemic agents and their applications in monotherapy or combination therapy.