Sum Of Constant Research Articles

Euler and the Cubic Basel Problem

In 1734, Leonhard Euler summed the infinite series of reciprocals of the squares, thereby solving a challenge known as the “Basel problem.” He later extended his method to find closed-form sums for the reciprocals of 4th, 6th, and other even powers. But those techniques did not yield a value for the sum of the reciprocals of the cubes. Here, we show how Euler tried to evaluate this series by transforming it into the sum of a strange constant and an even stranger integral.

Magnetostatic dipolar anisotropy energy and anisotropy constants in arrays of ferromagnetic nanowires as a function of their radius and interwall distance

Magnetostatic dipolar anisotropy energy and the total dipolar anisotropy constant, , in periodic arrays of ferromagnetic nanowires have been calculated as a function of the nanowire radius, the interwall distance of the nanowires in the arrays and the geometry of the array (square or hexagonal), by using a realistic atomistic model and the Ewald method. The simulated nanowires have a radius size up to 175 Å that corresponds to 31 500 atoms, and the simulated nanowire arrays have interwall distances between 35 and 3000 Å. The dependence of total magnetostatic dipolar anisotropy constant on the nanowire radius, their interwall distance and the type of array symmetry has been analyzed. The total dipolar anisotropy constant, which is the sum of the intrananowire dipolar anisotropy constant, , due to the dipolar interactions inside an isolated nanowire and the main responsible of the shape anisotropy, and of the internanowire dipolar anisotropy constant, , due to the magnetostatic dipolar interactions among nanowires in the array, have been calculated and compared with the magnetocrystalline anisotropy constant for three nanowire compositions and their crystalline structures. The simulations of the nanowire arrays with large interwall distances have been used to calculate the intrananowire anisotropy constant, , and to analyze the competition between the intrananowire, internanowire and magnetocrystalline anisotropies. According to some magnetic theories, the ratio equals to the areal filling fraction of a nanowire array. Present calculations indicate that the equation for the areal filling fraction matches perfectly for any interwall distance and radius of Ni and Co nanowire arrays. This first equation is used to write a general equation that relates the radius and interwall distance of nanowire arrays with the intrananowire, internanowire and magnetocrystalline anisotropies. This general equation allows to design the geometry of nanowire arrays with the desired orientation of the easy magnetization axis.

Synergistic effects of photocatalytic and electrocatalytic oxidation based on a three-dimensional electrode reactor toward degradation of dyes in wastewater

Degradation processes and kinetics of methyl orange (MO) by photocatalytic oxidation (PCO), electrocatalytic oxidation (ECO), and photoelectrocatalytic oxidation (PECO) were investigated using a three-dimensional electrode reactor with TiO2/Ti electrode as anode and TiO2 immobilized on columnar activated carbon (TiO2/CAC) as packed bed particle electrodes. The synergistic effects of PCO and ECO under different anode bias voltages were studied. UV irradiation for generating electron-hole pairs and external bias voltage for promoting the separation of photogenerated holes and electrons were conducive to achieving a synergistic effect during the PECO process, thereby significantly improving the efficiency of degradation. Moreover, under an anode bias voltage of 1.0 V, the degradation efficiency of MO in PECO process reached 98.76% at 35 min, which was much higher than that of in PCO (62.43%) and in ECO (33.93%) processes. The degradation rate constant of the PECO was estimated to be 0.1354 min−1, which was significantly higher than the sum of degradation rate constant of the PCO (0.0260 min−1) and ECO process (0.0114 min−1). This novel three-dimensional electrode reactor has excellent efficiency of degradation by PECO process and shows a great potential application in wastewater treatment.

Numerical Estimation of the Pseudo-Jahn-Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules.

The pseudo-Jahn-Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.

Cosmological evolution with the cubic order field derivative coupling

We investigate cosmological evolution in the scalar–tensor theory with the field derivative coupling to the double-dual of the Riemann tensor (the cubic-type theory). The theory can be seen as the straightforward extension of the scalar–tensor with the quadratic order field derivative coupling to the Einstein tensor (the quadratic-type theory). Both the field derivative couplings to the Einstein tensor and the double-dual of the Riemann tensor have been argued in terms of the successful realization of the self-tuning of the cosmological constant within the Horndeski theory. Assuming the constant potential given by the sum of the cosmological constant and the quantum vacuum energy, the shift symmetry for the scalar field and no matter fields, in the spatially-flat Friedmann–Lemaitre–Robertson–Walker spacetime, we can reduce the set of the field equations to the first-order ordinary nonlinear differential equation for the Hubble parameter, showing the existence of the self-tuned and runaway de Sitter solutions, in addition to the standard de Sitter solutions in general relativity and the finite Hubble singularities which can be reached within the finite time. We then argue the possible cosmological evolution in terms of the values of the effective cosmological constant, the kinetic coupling constants and the initial Hubble parameter. Although the behavior of the universe around each of the de Sitter solutions as well as the finite time singularities is very similar in both theories, we find that the crucial difference appears in terms of no bounce or turnaround behavior across the vanishing Hubble parameter as well as no limitation for the range of the Hubble parameter in the cubic-type theory.

Cosmological constraints on superconducting dark energy models

We consider cosmological tests of a scalar-vector-tensor gravitational model, in which the dark energy is included in the total action through a gauge invariant, electromagnetic type contribution. The ground state of dark energy, corresponding to a constant potential $V$ is a Bose-Einstein type condensate with spontaneously broken U(1) symmetry. In another words dark energy appears as a massive vector field emerging from a superposition of a massless vector and a scalar field, the latter corresponding to the Goldstone boson. Two particular cosmological models, corresponding to pure electric and pure magnetic type potentials, respectively are confronted with Type IA Supernovae and Hubble parameter data. In the electric case good fit is obtained along a narrow inclined stripe in the $\Omega _{m}-\Omega _{V}\,$ parameter plane, which includes the $\Lambda $CDM limit as the best fit. The other points on this admissible region represent superconducting dark energy as a sum of a cosmological constant and a time-evolving contribution. In the magnetic case the cosmological test selects either i) parameter ranges of the superconducting dark energy allowing for the standard baryonic plus dark matter or ii) a unified superconducting dark matter and dark energy model, additionally including only the baryonic sector.

Greedy versus social: resource-competing oscillator network as a model of amoeba-based neurocomputer

A single-celled amoeboid organism, the true slime mold Physarum polycephalum, exhibits rich spatiotemporal oscillatory behavior and sophisticated computational capabilities. The authors previously created a biocomputer that incorporates the organism as a computing substrate to search for solutions to combinatorial optimization problems. With the assistance of optical feedback to implement a recurrent neural network model, the organism changes its shape by alternately growing and withdrawing its photosensitive branches so that its body area can be maximized and the risk of being illuminated can be minimized. In this way, the organism succeeded in finding the optimal solution to the four-city traveling salesman problem with a high probability. However, it remains unclear how the organism collects, stores, and compares information on light stimuli using the oscillatory dynamics. To study these points, we formulate an ordinary differential equation model of the amoeba-based neurocomputer, considering the organism as a network of oscillators that compete for a fixed amount of intracellular resource. The model, called the “Resource-Competing Oscillator Network (RCON) model,” reproduces well the organism’s experimentally observed behavior, as it generates a number of spatiotemporal oscillation modes by keeping the total sum of the resource constant. Designing the feedback rule properly, the RCON model comes to face a problem of optimizing the allocation of the resource to its nodes. In the problem-solving process, “greedy” nodes having the highest competitiveness are supposed to take more resource out of other nodes. However, the resource allocation pattern attained by the greedy nodes cannot always achieve a “socially optimal” state in terms of the public cost. We prepare four test problems including a tricky one in which the greedy pattern becomes “socially unfavorable” and investigate how the RCON model copes with these problems. Comparing problem-solving performances of the oscillation modes, we show that there exist some modes often attain socially favorable patterns without being trapped in the greedy one.

Aetherizing Lambda: Barotropic fluids as dark energy

We examine the class of barotropic fluid models of dark energy, in which the pressure is an explicit function of the density, p = f(\rho). Through general physical considerations we constrain the asymptotic past and future behaviors and show that this class is equivalent to the sum of a cosmological constant and a decelerating perfect fluid, or "aether", with w_{AE}\ge0. Barotropic models give substantially disjoint predictions from quintessence, except in the limit of \LambdaCDM. They are also interesting in that they simultaneously can ameliorate the coincidence problem and yet "predict" a value of w\approx-1.

K-essence model of inflation, dark matter, and dark energy

We investigate the possibility for $k$-essence dynamics to reproduce the primary features of inflation in the early universe, generate dark matter subsequently, and finally account for the presently observed acceleration. We first show that for a purely kinetic $k$-essence model the late-time energy density of the universe when expressed simply as a sum of a cosmological constant and a dark matter term leads to a static universe. We then study another $k$-essence model in which the Lagrangian contains a potential for the scalar field as well as a noncanonical kinetic term. We show that such a model generates the basic features of inflation in the early universe, and also gives rise to dark matter and dark energy at appropriate subsequent stages. Observational constraints on the parameters of this model are obtained.

A study on synergistic effect of photocatalytic ozonation for carbaryl degradation

The combination of UVA radiation and ozone, in the presence of titanium dioxide, has been investigated as a potential destructive technology for the treatment of pesticide wastewaters. The contribution of single ozonation (O 3), photolytic ozonation (O 3/UV), and photocatalysis (TiO 2/UV) to degradation of carbaryl, a carbamate pesticide is assessed and compared with that of combined photocatalytic ozonation process (TiO 2/UV/O 3). For 40 mg/L of carbaryl (500 mL) at pH 6 and with 0.28 g/h of ozone and 1 g/L of TiO 2, 92% COD reduction was achieved in 180 min. Under this experimental condition, 76.5% TOC removal and increase of BOD 5/COD ratio to 0.38 was also observed. The synergistic effect occurs in the combined photocatalytic ozonation process which is proved by the significant improvement in the mineralization rate constant (0.09 min –1) when compared with the sum of mineralization rate constant of photocatalysis and ozonation (0.05 min –1). Further synergistic effect was noticed at acidic and neutral pH, but synergism was lost at alkaline pH due to faster self decomposition of ozone.

A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares

We introduce a modification of the linear ARCH (LARCH) model (Giraitis, Robinson, and Surgailis (2000)) - a special case of Sentana's (1995) quadratic ARCH (QARCH) model - for which the conditional variance is a sum of a positive constant and the square of an inhomogeneous linear combination of past observations. Necessary and sufficient conditions for the existence of a stationary solution with finite variance are obtained. We give conditions under which the stationary solution with infinite fourth moment can exhibit long memory, the leverage effect, and a Lévy-stable limit behavior of partial sums of squares.

A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares

We introduce a modification of the linear ARCH (LARCH) model (Giraitis, Robinson, and Surgailis (2000)) - a special case of Sentana's (1995) quadratic ARCH (QARCH) model - for which the conditional variance is a sum of a positive constant and the square of an inhomogeneous linear combination of past observations. Necessary and sufficient conditions for the existence of a stationary solution with finite variance are obtained. We give conditions under which the stationary solution with infinite fourth moment can exhibit long memory, the leverage effect, and a Lévy-stable limit behavior of partial sums of squares.

주택 실내.외 이산화질소 측정을 이용한 환기량 및 발생량 추정

Indoor air quality can be affected by indoor sources, ventilation, decay and outdoor levels. Although technologies exist to measure these factors, direct measurements are often difficult. The purpose of this study was to develop an alternative method to characterize indoor environmental factors by multiple indoor and outdoor measurements. Using a mass balance model and regression analysis, penetration factor (ventilation rate divided by the sum of ventilation rate and deposition constant) and source strength factor (source strength divided by the sum of ventilation rate and deposition constant) were calculated using multiple indoor and outdoor measurements. Subsequently, the ventilation rate and <TEX>$NO_2$</TEX> generation rate were estimated. Mean of ventilation rate was 1.41 ACH in houses, assuming a residential N02 deposition constant of 0.94 <TEX>$hr^{-1}$</TEX>. Mean generation rate of <TEX>$NO_2$</TEX> was 16.5 ppbv/hr. According to house characterization, inside smoking and family number were higher <TEX>$NO_2$</TEX> generation rates, and apartment was higher than single-family house. In conclusion, indoor environmental factors were effectively characterized by this method using multiple indoor and outdoor measurements.

주택에서 Box Model을 이용한 평균 환기율 및 이산화질소 발생량 추정

Indoor air quality is affected by source strength of pollutants, ventilation rate, decay rate, outdoor level, and so on. Although technologies measuring these factors exist directly, direct measurements of all factors are not always practical in most field studies. The purpose of this study was to develop an alternative method to estimate these factors by application of multiple measurements. For the total duration of 30 days, daily indoor and outdoor <TEX>$NO_2$</TEX> concentrations were measured in 30 houses in Brisbane, Australia, and for 21 days in 40 houses in Seoul, Korea, respectively. Using a box model by mass balance and linear regression analysis, penetration factor (ventilation divided by sum of air exchange rate and deposition constant) and source strength factor (emission rate divided by sum of air exchange rate and deposition constant) were calculated, Sub-sequently, the ventilation and source strength were estimated. In Brisbane, the penetration factors were <TEX>$0.59\pm0.14$</TEX> and they were unaffected by the presence of a gas range. During sampling period, geometric mean of natural ventilation was estimated to be <TEX>$l.l0\pm1.5l$</TEX> ACH, assuming a residential <TEX>$NO_2$</TEX> decay rate of 0.8 <TEX>hr^{-1}$</TEX> in Brisbane. In Seoul, natural ventilation was <TEX>$1.15\pm1.73$</TEX> ACH with residential <TEX>$NO_2$</TEX> decay rate of 0.94 <TEX>hr^{-1}$</TEX> Source strength of <TEX>$NO_2$</TEX> in the houses with gas range <TEX>$(12.7\pm9.8$</TEX> ppb/hr) were significantly higher than those in houses with an electric range <TEX>$(2.8\pm2,6$</TEX> ppb/hr) in Brisbane. In Seoul, source strength in the houses with gas range were <TEX>$l6.8\pm8.2$</TEX> ppb/hr. Conclusively, indoor air quality using box model by mass balance was effectively characterized.

Characterization of indoor air quality using multiple measurements of nitrogen dioxide.

Indoor air quality can be affected by indoor sources, ventilation, decay and outdoor levels. Although technologies exist to measure these factors, direct measurements are often difficult. The purpose of this study was to develop an alternative method to characterize indoor environmental factors by multiple indoor and outdoor measurements. Daily indoor and outdoor NO2 concentrations were measured for 30 consecutive days in 28 houses in Brisbane, Australia, and for 21 consecutive days in 37 houses in Seoul, Korea. Using a mass balance model and regression analysis, penetration factor (ventilation rate divided by the sum of ventilation rate and deposition constant) and source strength factor (source strength divided by the sum of ventilation rate and deposition constant) were calculated using multiple indoor and outdoor measurements. Subsequently, the ventilation rate and NO2 source strength were estimated. Geometric means of ventilation rate were 1.44 air change per hour (ACH) in Brisbane, assuming a residential NO2 deposition constant of 1.05/h, and 1.36 ACH in Seoul, with the measured residential NO2 deposition constant of 0.94/h. Source strengths of NO2 were 15.8 +/- 18.2 and 44.7 +/- 38.1 microg/m3/h in Brisbane and Seoul, respectively. In conclusion, indoor environmental factors were effectively characterized by this method using multiple indoor and outdoor measurements.

EFFECTS OF FACIAL COLD STIMULATION ON PULMONARY VO2 AND FEMORAL ARTERY BLOOD FLOW KINETICS DURING REPEATED BOUTS OF HEAVY KNEE EXTENSION EXERCISE

We investigated the effects of delayed vagal withdrawal to the circulation induced by facial cold stimulation (CFS) on the temporal profile between pulmonary O2 and femoral artery blood flow (BFfa) during repeated bouts of heavy knee extension (KE) exercise. Six healthy subjects (aged 22–44 years) volunteered to participate in this study. The control protocol consisted of two consecutive 6-min KE exercise bouts in a supine position (work rate: 75 % of peak power) separated by 6-min baseline rest (L1-ex to L2-ex). In the experimental protocol, CFS was applied with cold gel-filled compresses to the face during 4 min (i.e., 1 min before to 3 min after the onset of exercise) in either 1st bout (S1-ex) or 2nd bout (S2-ex) of repeated exercise. During the protocol, a Doppler ultrasound technique (3.5 MHz; EUB-415: Hitachi Medico) continuously measured right BFfa. Each protocol was performed at least 6 times to accurately characterize the kinetics derived from mono-exponential fitting. In the control protocol, O2-kinetics for the 2nd bout were faster than those for the 1st bout [the mean ± S.D. of the mean response time (MRT, sum of delay and time constant), L1-ex: 78.9 ± 15.8 s, L2-ex: 67.9 ± 12.3 s, P < 0.05]. The effects of CFS on the circulation were variable. Hear rates during CFS were consistently lower than those in a control condition whereas no concomitant reductions were noticed in BFfa after the onset of exercise. There were no significant O2 MRT differences between either L1-ex vs. S1-ex [69.0 ± 9.5 s] or L2-ex vs. S2-ex [65.8 ± 9.4 s]. It was concluded that increased vagal withdrawal may delay the central circulatory response, but does not alter the peripheral response to working limb after the onset of heavy exercise. Supported in part by Grant-in-Aid for Scientific Research from The Ministry of Education, Science, Sports and Culture in Japan (#11680026, #12680048, and #12554039).

Delayed vagal withdrawal slows circulatory but not oxygen uptake responses at work increase.

The effect of delayed vagal activity withdrawal on cardiorespiratory responses at an increase in workload was examined. Eleven volunteers (21 +/- 3 yr, 66 +/- 4 kg) performed cycle ergometer exercise at a work rate corresponding to 80% of ventilatory threshold after 3 min of unloaded cycling. Facial stimulation was given by applying a vinyl bag filled with cold water (3-5 degrees C) to the face 1 min before to 1 min after the increase in workload (S2 trial) or no stimulation was given (Nr trial). Oxygen uptake (VO2), heart rate (HR), and cardiac output (Q) were continuously recorded in four transitions for each trial. Data were averaged for each subject and trial. Mean response time (MRT, sum of delay and time constant) was calculated with monoexponential fitting. Facial stimulation induced acute bradycardia (-10 +/- 5 beats/min in S2 trial). The MRT of HR and Q was significantly longer in the S2 trials (46 +/- 35 and 37 +/- 23 s) than in the Nr trials (26 +/- 18 and 28 +/- 19 s, respectively), but no significant change in VO2 MRT was shown (36 +/- vs. 38 +/- 12 s). These findings suggest that increased vagal activity delays the central circulatory responses, which does not alter the VO2 kinetics at the onset of stepwise increase in workload. The maintenance of VO2 kinetics during acute bradycardia may either reflect the fact that some intramuscular processes (such as oxidative enzyme inertia) limit VO2 kinetics or alternatively that increased sympathetic vasoconstriction at some remote site defends exercising muscle blood flow.

The effect of free DNA on the interactions of the estrogen receptor bound to hormone, partial antagonist or pure antagonist with target DNA.

Interactions between the lamb uterine estrogen receptor occupied by estradiol, 4-hydroxytamoxifen (a non-steroidal partial estrogen antagonist) or ICI 164,384 (a steroidal pure estrogen antagonist), and the vitellogenin A2 estrogen-response element (vit ERE) were compared using a biotinylated 25-base all-palindromic double-stranded oligonucleotide, containing vit ERE (b-ERE), which allowed isolation of the b-ERE.receptor.[3H]ligand assembly on streptavidin-Sepharose. The results of saturation analyses of the three receptor.[3H]ligand complexes by increasing amounts of b-ERE were quite similar for the proportion of complexes able to interact with b-ERE (which varied from 30% to 65% according to experiments) and for the equilibrium dissociation constant [Kd (0 degree C) approximately 1.2 nM, assuming that the receptor interacted as a dimer with b-ERE]. With each ligand, receptor binding to ERE did not change the rate of ligand dissociation from the receptor at 20 degrees C. The rate of estrogen receptor dissociation from b-ERE, measured at 20 degrees C in the presence of a given concentration of ERE, did not vary according to the ligand bound to the receptor; however, this dissociation rate increased linearly over the ERE concentration range (0.5-10 microM). The experimental rate constant (k-) of estrogen receptor dissociation from b-ERE appeared to be the sum of the basal dissociation-rate constant (k degrees - approximately 0.011 min-1), corresponding to spontaneous dissociation which would occur in the absence of ERE, and of the ERE-induced dissociation-rate constant, proportional to the used concentration of ERE (ki- approximately 4500 CERE M-1 min-1, where CERE is the molar concentration of ERE). Non-target DNA also induced receptor dissociation from b-ERE, but its efficiency was 6-10-fold lower than that of ERE. We conclude that, the two antiestrogens are as efficient as estradiol in promoting estrogen receptor binding to a single vit ERE; the low or nil ability of antiestrogens to induce estrogenic responses is probably not linked with the receptor DNA-binding step; DNA binding does not seem to affect the conformation of the filled hormone-binding site of the receptor at 20 degrees C; interactions of receptor dimers with DNA seems to proceed by direct transfer of receptor dimers between DNA strands.

An Optical Adaptive Device and Its Application to a Competitive Learning Circuit

A mechanism suppressing the divergence of synaptic weights should be added to the network performing unsupervised learning algorithms with the Hebbian rule. In order to realize competitive learning in hardware, a synaptic connection circuit keeping a sum of synaptic weights constant was fabricated with the complementary field effect transistor (CMOS) floating gate process. The synaptic weights of each neuron were varied by applying the optical correction signals. The sum of synaptic weights was kept constant and the weights were memorized in a nonvolatile manner. A primitive competitive learning circuit was constructed with the synaptic connection circuits and a winner-take-all (WTA) circuit. The self-organization of the competitive circuit was confirmed experimentally and by means of simulations. The limitation of operating range and the feasibility of large-scale integration were discussed.

Stochastic Log Price, Land Value, and Adaptive Stand Management: Numerical Results for California White Fir

Abstract This paper presents an adaptive management formulation for determining the timing and intensity of thinning and the time of clearcut for stands with any age structure and with stochastic log prices. In contrast to previous timber management studies with stochastic prices, the formulation allows the determination of the best time to switch from forestry to another land use or from selection harvesting to plantation forestry. Harvests are determined with a piecewise linear function that relates harvest intensity and stand value. The parameters of the function include its slope, location, and length. Optimal parameter values are determined using stochastic simulation. Delivered log price is a stationary process that is the sum of a deterministic constant and a normally distributed random error. Numerical results are presented for young and mature stands of California white fir [Abies concolor (Gord. &amp; Glend.) Lindl. (Iowiana [Gord.])]. The results include when to terminate forestry and switch land use. The expected time of clearcut is inversely related to the bare land value. The effect of price variation on the time of clearcut depends on land value. For low land values, increasing price variation decreases the expected time of clearcut; for high land values, the effect of price variation is reversed. The results include estimates of the relative economic efficiency of plantation versus uneven-age forestry. The size of trees in the initial stand rather than price variation phys the critical role in determining the relative economic returns. Because the results are dependent on the assumption that the price process is stationary, caution should be used in extending the results beyond the case presented here. For. Sci. 37(5):1224-1238.