On restricting Cauchy–Pexider functional equations to submanifolds

Sufficient geometric conditions are given which determine when the Cauchy–Pexider functional equation f(x)g(y) = h(x + y) restricted to x, y lying on a hypersurface in ${\mathbb{R}^d}$ has only solutions which extend uniquely to exponential affine functions ${\mathbb{R}^d \to \mathbb{C}}$ (when f, g, h are assumed to be measurable and non-trivial). The Cauchy–Pexider-type functional equations ${\prod_{j=0}^df_j(x_j)=F(\sum_{j=0}^dx_j)}$ for ${x_0, \ldots,x_d}$ lying on a curve and ${f_1(x_1)f_2(x_2)f_3(x_3)=F(x_1+x_2+x_3)}$ for x ₁, x ₂, x ₃ lying on a hypersurface are also considered.     

The one dimensional Compartmentalised Knapsack Problem: A case study

The Compartmentalised Knapsack Problem (CKP) is similar to the ordinary Knapsack Problem except that items to be packed belong to separate classes, and items can only be packed, in knapsack compartments, amongst items in their own class. This paper addresses a case study in the cutting of steel rolls in which the CKP arises. The rolls are cut in two-phases: the first phase produces sub-rolls (compartments) which are, after reducing the thickness, cut in a second phase to produce ribbons (a class consists of ordered items with the same thickness). Finally, two methods of solving CKP are presented, and these are used to generate columns in the classical linear optimisation model of Gilmore and Gomory. Results of computational experiments are presented.     

Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism

The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.     

Naturalness and Theoretical Constraints on the Higgs Boson Mass

Arbitrary regularization dependent parameters in Quantum Field Theory are usually fixed on symmetry or phenomenology grounds. We verify that the quadratically divergent behavior responsible for the lack of naturalness in the Standard Model (SM) is intrinsically arbitrary and regularization dependent. While quadratic divergences are welcome for instance in effective models of low energy QCD, they pose a problem in the SM treated as an effective theory in the Higgs sector. Being the very existence of quadratic divergences a matter of debate, a plausible scenario is to search for a symmetry requirement that could fix the arbitrary coefficient of the leading quadratic behavior to the Higgs boson mass to zero. We show that this is possible employing consistency of scale symmetry breaking by quantum corrections. Besides eliminating a fine-tuning problem and restoring validity of perturbation theory, this requirement allows to construct bounds for the Higgs boson mass in terms of $\delta m^{2}/m^{2}_{H}$ (where m _H is the renormalized Higgs mass and δm ² is the 1-loop Higgs mass correction). Whereas $\delta m^{2}/m^{2}_{H}<1$ (perturbative regime) in this scenario allows the Higgs boson mass around the current accepted value, the inclusion of the quadratic divergence demands $\delta m^{2}/m^{2}_{H}$ arbitrarily large to reach that experimental value.     

Assessment of environmental noise and its effect on neonates in a Neonatal Intensive Care Unit

A method for analyzing the influence of noise on newborns is proposed. The method consists of defining three different types of time interval (quiet, noisy and nursing) and, for each period, environmental noise levels, heart rate, mean arterial pressure and oxygen saturation is continuously measured. The statistical analysis of the influence of the equivalent noise level, rather than instantaneous noise level, on the behavior of the physiological variables is carried out. Great influence of noise is found by using this method, which is also easily translatable to other intensive care units as actual noise conditions are used in the investigation. Moreover, episodes of Bradycardia, Hypoxia and Hypertension are easily related to simultaneous direct nursing activity or a short but high enough noise event, suggesting that both sustained noisy environment and isolated peak noises lead to the alteration of the physiological variables.     

Consequences of magnetic aging for iron losses in electrical steels

Electrical steels, when submitted to operation, present continuous decrease of their magnetic properties, depending on the carbon content. This effect is attributed to the increase of the size of carbides, a process also known as coarsening or Ostwald Ripening. Loss separation can offer a better understanding of this phenomenon. Experimental results show that all effect of aging is inside the hysteresis loss component, with the excess losses unaffected. The carbon content in electrical steels should be less than 25 ppm to avoid magnetic aging.     

Early iNOS impairment and late eNOS enhancement during reperfusion following 2.49 MHz continuous ultrasound exposure after ischemia

ObjectiveIschemia reperfusion (IR) injury, occurring during heart attacks, hemorrhagic shock, and bypass and transplant surgeries, impairs microcirculatory function and nitric oxide (NO) synthesis. We report the regulation of endothelial and inducible NO synthase (eNOS and iNOS) proteins as a consequence of the application of continuous mode diagnostic frequency ultrasound application following IR injury.MethodsAnimals were assigned to one of five groups for microcirculatory assessment or Western blot analysis (WB) as follows: (1) IR+iNOS inhibition (1400W); and (2) IR+1400W+ultrasound for microcirculatory assessment, (3) Control; (4) IR; and (5) IR+ultrasound for WB. Functional capillary density and microvascular diameter, flow velocity, and flow were monitored for microcirculatory assessment. Skin tissue samples were harvested for WB. 2.49 MHz continuous ultrasound was used for application.ResultsBoth the inhibition of iNOS alone and iNOS inhibition with ultrasound irradiation positively influenced the microcirculation of observed animals relative to baseline values. Ultrasound exposure resulted in a significant production of eNOS protein in skin tissue harvested 24 h into reperfusion (p < 0.01). iNOS levels from the same tissue of ultrasound exposed animals were found to be significantly decreased 0.5 h into reperfusion (p < 0.05).ConclusionProtection from lasting IR injury effects in the microcirculation, with continuous mode diagnostic frequency ultrasound, results from augmented eNOS protein levels during late reperfusion. Ultrasound inhibited iNOS protein production during early reperfusion may also confer protection from IR injury.     

Pressure dependence of dielectric constant,elastic constants,and lattice parameters of the Y3(Ga,Al)5O12 host

Atomistic simulations were performed to investigate the lattice parameters, dielectric constant, and elastic constants of Y₃(Ga_xAl_5−x)O₁₂ (x = 1, 2, 3, 4, 5) structures. The calculated lattice parameters and elastic constants are in good agreement with those in available experimental results. The pressure dependence of all studied quantities was investigated. In general, a change in the behavior of all studied quantities is found when the Ga concentration becomes more than that of the aluminum (Al) in Y₃(Ga_xAl_5−x)O₁₂ (x = 1, 2, 3, 4, 5) structures.     

Importance of multiple-scattering phenomena in XAS structural determinations of [Ni(CN)4]2- in condensed phases

A quantitative analysis of the XAS spectra of the tetracyanonickelate complex [Ni(CN)4]2- has been carried out. The simultaneous study of the EXAFS and XANES regions yielded complementary information regarding the geometric and electronic structures of the complex. XANES spectra were modeled by applying recently developed self-consistent, full multiple-scattering algorithms in the FEFF8 code (version 8 x 34). XANES spectra for clusters of different sizes (from 9 to 125 atoms) were computed and compared with experimental spectra. This region of the spectra was proportional to a broadened Ni p-density of states diagram above the Fermi level. Although the main features of the XANES spectra were reasonably reproduced by computations, the weak dependence of the theoretical spectra on cluster size contrasts with the close similarity between the experimental spectra of the solid and solution systems. Because of the special geometry of the complex, calculations with polarized light parallel and perpendicular to the molecular plane were carried out, yielding a reasonable reproduction of the experimental data from another report for cluster sizes equal to or higher than 45 atoms. The highly symmetric square planar structure of the complex was found to be responsible for the unusual amplitude of the multiple-scattering (MS) contributions to the EXAFS spectra. Spectra in this region were fitted using the FEFFIT EXAFS analysis program, taking into account only the MS paths that simultaneously have both a high amplitude, as calculated with the ab initio code FEFF, and a small Debye-Waller factor, as estimated by the independent-vibration approximation model. Fitting results yielded very similar structures for the Ni2+ complex in the solid state and in solution, though the larger Debye-Waller factors found for the solid suggest higher static disorder in this state.