Root Law Research Articles

CHANDRAVIEW OF PULSAR WIND NEBULA TORI

The results from a systematic study of eleven pulsar wind nebulae with a torus structure observed with the Chandra X-ray observatory are presented. A significant observational correlation is found between the radius of the tori, r, and the spin-down luminosity of the pulsars, Edot. A logarithmic linear fit between the two parameters yields log r = (0.57 +- 0.22) log Edot -22.3 +- 8.0 with a correlation coefficient of 0.82, where the units of r and Edot are pc and ergs s^-1, respectively. The value obtained for the Edot dependency of r is consistent with a square root law, which is theoretically expected. This is the first observational evidence of this dependency, and provides a useful tool to estimate the spin-down energies of pulsars without direct detections of pulsation. Applications of this dependency to some other samples are also shown.

Electrospray of a very viscous liquid in a dielectric liquid bath

AbstractNumerical computations and order-of-magnitude estimates are used to analyze a jet of a very viscous liquid of finite electrical conductivity that is injected at a constant flow rate in an immiscible dielectric liquid under the action of an electric field. The conditions under which the injected liquid can form an elongated meniscus with a thin jet issuing from its apex (a cone-jet) are investigated by computing the flow, the electric field, and the transport of electric charge in the meniscus and a leading region of the jet. The boundaries of the domain of operation of the cone-jet mode are discussed. The current transfer region determining the electric current carried by the jet is analyzed taking into account the viscous drag of the dielectric liquid surrounding the jet. Conditions under which the electric current/flow rate characteristic follows a square root law or departs from it are discussed.

한국기술혁신연구의 인용문헌 법칙과 의사 영향력지수

계량서지학은 오랫동안 잘 정의된 과학저널의 기초 위에서 구축되었다. 그러나 한국의 기술혁신연구의 역사는 짧고 다른 분야에 비해 연구범위도 다양하다. 따라서 우리는 한국의 기술혁신연구에서도 전통적인 계량서지학의 법칙들이 적용되는지를 고찰하고자 한다. 한편 전통적인 법칙과 함께 멱함수 법칙의 설명력을 비교한다. 영향력지수와 관련하여, 한국의 기술혁신연구에 기여 정도를 측정하는 의사 영향력지수를 제안한다. 연구자의 생산성을 측정하기 위해 사용되는Lotka's law와 Bradford's law가 적용됨을 확인했으나, Nicholls(1998)와 마찬가지로 Price's Square Root law가 유효하지 않았다. 저널에 대한 인용의 측면에서는Garfield의 법칙 역시 적절하지 않았다. 다만 멱함수 법칙은 저자, 저널, 논문 및 단행본 모두에서 잘 적용됨을 확인하였다. 이전 연구에서 추정된1.5에서3사이의 범주와 유사하게 한국의 기술혁신연구에서도 1.6에서 3.5사이의 수치가 추정된 것이다. 의사 영향력지수(quasi-impact factor)를 본 연구에 적용한 결과, 피인용도가 높은 저널 집단의 한국기술혁신연구에 대한 영향력은 국제적 기술혁신연구에 비하여 그 정도가 약한 것으로 나타났다. Existing bibliometric laws have been established on the basis of well defined science journals with a long history. However, the history of technology innovation research in Korea is young and the scope of the research is diverse compared with other fields. The main purpose of this research can be summarized as follows : Can the traditional bibliometric laws be used to explain the young and diverse data derived from technology innovation studies in Korea. Second, we want to compare the explain ability of the power law, compared with the traditional laws in the field. Third, we propose a quasi index related to the well-known impact factor to measure the contribution of a journal or a group of journals to the development of innovation research in Korea. We confirmed Lotka's and Bradford's laws which are used to measure the productivity of researchers, but we could not support the validity of Price's Square Root law as Nicholls (1998) could not. On the citations to journals, Garfield's laws is not observed. However, the power law fits well the citations to author, journal, article, and book. The estimated parameters between 1.6 and 3.5 are similar to the values in the range of 1.5 and 3 in previous studies. Finally the quasi index shows that the influence of international leading journals on innovation research in Korea is weaker than on innovation studies in the world.

Utility Optimization Based on MSE for Parallel Broadcast Channels: The Square Root Law

In order to design efficient online resource allocation algorithms, convexity of the underlying optimization problem is an important prerequisite. This paper covers two resource allocation problems: the sum-power constrained utility maximization and the sum-power minimization for minimum utility requirements for parallel broadcast channels. We derive a new class of utility functions for which both optimization problems can be transformed into convex representations and give necessary and sufficient conditions for the optimum solution of the original non-convex problems with regard to power. We thereby extend the known log-convexity class for which convex representations can be found and, by introducing the square-root criteria, present a straight forward test to check whether arbitrary utility functions belong to our class. For the new class of utility functions we present simple algorithms which operate in the non-convex domain, prove convergence to the global optimum and evaluate their performance by simulations. Besides, the paper reveals some insights on the general structure of the mean square error region and thereby disproves a former result.

Quadratic root law (one of the store models) to change the rent of the houses

Most of houses' owners try to increase the houses' rental prices from time to time. However this increase will be taken place, but the real income of the owners declines, that is because of many different costs that the owner will carry out. This research includes the following question "How long should the houses' owners rise the houses' rental prices?" The Economic Optimal Quantity size (EOQ) formula used to derive two equations, first for houses have constant value, second for houses have increasing market value during the time. Moreover, these two equations determine the increase rate of houses' rental price and the optimal period of changing the rental price for both situations.

Influence of sodium dodecyl sulfate on swelling, erosion and release behavior of HPMC matrix tablets containing a poorly water-soluble drug

The effect of sodium dodecyl sulfate (SDS) on the swelling, erosion and release behavior of HPMC matrix tablets was examined. Swelling and erosion of HPMC matrix tablets were determined by measuring the wet and subsequent dry weights of matrices. The rate of uptake of the dissolution medium by the matrix was quantified using a square root relationship whilst the erosion of the polymer was described using the cube root law. The extent of swelling decreased with increasing SDS concentrations in the dissolution medium but the rate of erosion was found to follow a reverse trend. Such phenomena might have been caused by the attractive hydrophobic interaction between HPMC and SDS as demonstrated by the cloud points of the solutions containing both the surfactant and polymer. Release profiles of nimodipine from HPMC tablets in aqueous media containing different concentrations of SDS were finally studied. Increasing SDS concentrations in the medium was shown to accelerate the release of nimodipine from the tablets, possibly due to increasing nimodipine solubility and increasing rate of erosion by increasing SDS concentrations in the dissolution medium.

Le redéploiement des stocks, une autre alternative à la maîtrise des coùts de transport

Store or transport? What to decide today as part of an approach to minimize logistics costs? The time for the multiplicity of deposits seemed over. From 1990 to 2006, it was clear that there was a marked decrease in the number of small storage sites, with depots gradually giving way to fewer but much larger warehouses. This tendency to reduce the number of storage places largely dominated for about fifteen years: the financial interest was particularly motivating. At the same time, we have seen the increase in the number of distribution platforms, a direct consequence of the development of just-in-time flow and an essential alternative for controlling transport costs. Today, due to the significant and lasting increase in transport costs, the legitimacy of the theory of centralization of warehousing, more precisely that of the Square Root Law, seems contested. Certain economic players (in particular distributors) have thus started to re-burst their stocks on several sites. The redeployment of storage, another possible alternative to controlling transport costs, is therefore underway. What exactly is it? The purpose of this article is to specify under which conditions a decentralization of stocks may become relevant.

Accurate analytical models for fractional pressure rise in constant volume combustion

Laminar burning velocities S L can be obtained from the pressure history in a constant volume combustion experiment. In the analysis of results, the relation between pressure and mass fraction burnt, x ( p ) , is crucial. The linear x ( p ) relation by Lewis and Von Elbe is still widely used. Yet, from their original work a more accurate relation for x ( p ) can be derived, as is demonstrated in this paper (“extended LvE”). In this work we introduce a two zone model that can be treated analytically, resulting in an x ( p ) -relation identical to “extended LvE”. We then extend our analytical approach to a multi-zone model, which is used to benchmark several other analytical x ( p ) relations. Results of the two-zone model are very close to the multi-zone results. Reported deviations between S L from bomb data and from other methods may be attributed to the limited accuracy of the linear x ( p ) relation, as is illustrated for stoichiometric methane–air combustion. Notably, for small x our new relation gives a factor of γ b / γ u difference in S L as compared to the linear one, which has long been assumed to be correct for small x. Our new x ( p ) result also leads to a new expression for the explosion constant K G in the cubic root law.

An extension of the square root law of TCP

Using probabilistic scaling methods, we extend the square root law of TCP to schemes which may not be of the AIMD type. Our results offer insight in the relationship between throughput and loss rate, and the time scale on which losses take place. Similar results are shown to hold in scenarios where dependencies between losses occur.

Is Baumol's ‘square root law’ still relevant? evidence from micro-level data

The purpose of the article is to test, from micro-level data, the complete general framework of the transaction demand for money a la Baumol. Controlling for selection bias, we distinguish two populations who exclusively withdraw cash from either ATM or bank counter, from a sample of French representative individuals. The estimation results show the existence of large economies of scale as well as a positive effect of ATM surcharge and ATM and bank counter density on cash holding. Moreover, contrary to what might be expected, we do not find evidence of the impact of risk on cash holding.

Simplified Model of the Dynamic Thermal Tuning Behavior of VCSELs

In this letter, a simplified thermal model is used to derive a closed-form expression for the frequency dependency of the current-to-wavelength tuning coefficient (FM response) of vertical-cavity surface-emitting lasers (VCSELs). It explains the experimentally observed square root law and shows very good agreement with measured FM responses of two different VCSEL types. It yields significantly improved accuracy compared to the usually assumed first-order low-pass model.

Effect of Polymer Concentration on the Dissolution Rates of Pioglitazone Hydrochloride

An emulsion of pioglitazone hydrochloride (drug) was prepared by mixing drug:polymer (gelatin) in different ratios of 1:0.5, 1:1, and 1:1.5 (wt/wt), respectively. These emulsions were used for the preparation of tablets of different composition. Tablet hardness increased with a decrease in concentration of polymer, while the percentage friability increased with an increase in polymer concentration in the tablet. The encapsulated tablet showed better sustained release than conventional tablets. The effect of concentration of polymer on dissolution rates of these tablets was studied using the Hixson-Crowell cube root law equation. The data obtained prove that the formulations are useful for a sustained release of pioglitazone hydrochloride, since the percentage released after 24 h was nearly 76%. The release of pioglitazone hydrochloride was influenced by the presence of polymer and different compositions of lactose. The tablet containing an emulsion of ratio 1:0.5 showed an excellent result of rate constant, better than conventional and other compositions.

Sucrose acetate isobutyrate as an In Situ forming system for sustained risperidone release

The objective of this study was to develop sustained-release sucrose acetate isobutyrate (SAIB) in situ formulations of risperidone for parenteral delivery. The formulations contained SAIB, solvent (anhydrous ethanol, ethyl lactate, or N-methyl-2-pyrrolidone), and additives such as polylactic acid (PLA). In vitro release profiles of risperidone from the SAIB formulations, which followed the Higuchii square root law, were obtained. An increase in SAIB content from 75% to 85% resulted in a reduction in the initial burst and the rate of risperidone release. The initial drug release could be increased by reducing the pH of the release medium and the release rate could be increased by an increase in drug loading. The burst release fell significantly from 20.0% to 3.5% following the inclusion of 10% (w/w) PLA in the formulations. In the case of this high viscosity depot system containing SAIB, anhydrous ethanol, PLA, and 25 mg/g risperidone, the in vivo biocompatible test results obtained support the use of SAIB as an injectable risperidone sustained-release formulation.

Experimental characterization of the frequency modulation behavior of vertical cavity surface emitting lasers

The frequency response of the current-to-wavelength tuning rate (FM response) was measured for two different vertical cavity surface emitting lasers (VCSELs) up to frequencies of 1MHz: GaAs-based VCSEL (763nm) and InP-based VCSEL (1853nm). Both of them show the same qualitative FM response behavior, which can be described by a square root law and therefore cannot be modeled by a first order low pass. The square root law behavior is a significant advantage for laser spectroscopy applications with VCSELs because the decrease of the current-to-wavelength tuning coefficient is less severe as in the case of the first order low pass.

Measuring the violence of dust explosions with the “20 l sphere” and with the standard “ISO 1 m 3 vessel” : Systematic comparison and analysis of the discrepancies

On the basis of a systematic testwork with a number of different dusts, the explosion indices as determined within the 20 l sphere and with the ISO-VDI 1 m 3 vessel have been compared. The repeatability has been assessed and since some systematic deviations appear a refined physical analysis of the explosion processes is developed. It appears in particular that the cube root law supposed to link both vessels is not verified. A striking illustration of this appears when a dust with a significant explosion severity inside the 20 l sphere is not even explosible in the larger vessel. It is strongly suggested that the ignition energy is forcing very significantly the explosion in the smaller vessel inducing several tens of Celsius degrees of preheating. It is shown also that the inner level of turbulence is decreasing very fast in the 20 l sphere during the flame development so that difficult-to-ignite mixtures would tend to burn at a lower combustion rate. It is further demonstrated that the major bias between the chambers can be explained and quantified with these elements. A correlation with the standard 1 m 3 vessel and a grid of interpretation of the data is proposed.

An approximation manpower planning model for after-sales field service support

Manpower planning is a key part of after-sales field service support with a service guarantee. Accurate field travel distance approximation presents a good opportunity to lower the manpower level. By explicitly considering the uncertainties, a state-dependent travel distance approximation model is presented and used to find the optimized manpower solution. A simulation model is developed to study the relationship between staffing level, travel distance, and percentage of customers serviced on time. Numerical results show that the proposed travel distance approximation model performs much better than the classical “square root law” and other models in the literature.

A variable bandwidth selector in multivariate kernel density estimation

Based on a random sample of size n from an unknown d-dimensional density f, the problem of selecting the variable (or adaptive) bandwidth in kernel estimation of f is investigated. The common strategy is to express the variable bandwidth at each observation as the product of a local bandwidth factor and a global smoothing parameter. For selecting the local bandwidth factor a method based on cluster analysis is proposed. This method is direct and intuitively appealing. For selecting the global smoothing parameter a method that is an adaptation of the frequency domain approach of selecting the fixed bandwidth in Wu and Tsai [2004. Root n bandwidths selectors in multivariate kernel density estimation. Probab. Theory Related Fields 129, 537–558] is used. For d = 1 and 2, extensive simulation studies have been done to compare the performance of our selector with the selectors of Abramson [1982. On bandwidth variation in kernel estimates—a square root law. Ann. Statist. 10, 1217–1223] and Sain and Scott [1996. On locally adaptive density estimation. J. Amer. Statist. Assoc. 91, 1525–1534] and Sain [2002. Multivariate locally adaptive density estimation. Comput. Statist. Data Anal. 39, 165–186], and the excellent performance of our selector at practical sample sizes is clearly demonstrated.

Pressure distribution in the neighborhood of a growing fracture with a constant wedge force

Exact solutions of the problem of the pressure field in the neighborhood of a hydraulic fracture developing in accordance with a square root law in a permeable porous medium with a constant wedge force acting on the fracture edges are constructed. A particular case admitting a self-similar formulation and an exact solution and, as a result, the fairly complete investigation, is considered. The solution constructed holds for an arbitrary self-similar pressure distribution over the fracture edges. The problem considered reduces to the solution of a mixed boundary-value problem for the Helmholtz equation. The solution found can be useful both in itself and for testing more universal numerical algorithms.

Is the Baumol's 'Square Root Law' Still Relevant? Evidence from Micro-Level Data

The objective is to test, from micro-level data, the complete general framework of the transaction demand for money a la Baumol established fifty years ago. The results confirm the relevancy of the Baumol's square root law while pointing out for the first time the impact of the subjective risk on cash holding.

A backward recursive algorithm for inventory lot-size models with power-form demand and shortages

In 1978, Barbosa and Friedman established a ‘general root law’ for power-form demand rate. Shortages are prohibited. However, in reality, shortages may occur and the planning time horizon is usually finite as the product life cycle is short. Therefore, the author here extends their inventory lot-size model to allow for shortages during a finite planning time horizon and propose an alternative algorithm in a backward manner to determine the optimal replenishment timing without using iterative search schemes. The study not only shows that the total relevant cost is a strictly convex function of the replenishment number, but also provides the condition for determining the optimal replenishment number. Finally, a numerical example is given for illustration.