A lower bound for the number of singular staturated main effect plans of anS m factorial

Summary A fraction consisting ofm(s−1)+1 observations taken atm(s−1)+1 treatment combinations of ans ^m factorial with the aim to estimate the mean and them(s−1), main effect single degree of freedom parameters is called a saturated main effect plan. If the design matrix of such a fraction is singular, then the fraction is called a singular saturated main effect plan. This paper presents a lower bound on the number of singular saturated main effect plans. Research supported by N.R.C. Grant No. A07204.     

Cantorian-fractal space-time and particles in a generalized magnetic field

In the fractal space-time theory the generalized precession, the generalized Stern–Gerlach experiment, the generalized Zeeman effect, the generalized Landau's levels and the generalized fractional quantum Hall effect are analyzed. The Cantorian structure of space-time implies the supplemental decreasing rate of the Ecliptic tilt, the “global” quantization in units of 36 km s⁻¹ and the filling factor ν=1/2n+1.     

A report on polarography of nitro derivatives of arylazopyrazoles

In an earlier communication¹ we reported our results on the effect of electron donating substituents on the polarographic reduction of 4-phenylazopyrazole. In this communication we report our results on the effect of an electron withdrawing substituent on the E_1/2 of 1-thiocarbamoyl-3, 5-diphenyl-4-phenylazopyrazole. The studies were carried out in non-aqueous medium due to water insoluble nature of these compounds.     

一类效应代数的态表示定理

1994年, Foulis和Bennett在表示不可精确测量的量子逻辑结构时引入了效应代数. 该文用直接构造的方法, 给出一类效应代数上的态表示定理. 即, 若Ω是紧的 Hausdorff 拓扑空间, 令E(Ω)={f: f∈C(Ω), 0≤f≤1}, 则φ 是(E(Ω),Ο, 0, 1) 上的态当且仅当Ω 上存在唯一的正则Borel 概率测度μ使得对每个f (E(Ω),Ο, 0, 1),φ (f)=∫_Ω f dμ.     

效应代数的表示理论

The aim of this paper is to characterize representable and weak representable effect algebras and establish a representation theory of effect algebras. An effect algebra E is said to be representable if there exists a Hilbert space H and a monomorphism π from E into the Hilbert space effect algebra ε(H) and it is said to be weakly representable if there exists an injective morphism from E into some ε(H). It is proved that an effect algebra E with the nonempty state space S(E) is representable if and only if x, y ∈ E, f(x)+f(y) ≤ 1 implies x⊕y is defined; it is weakly representable if and only if the state space S(E) separates the points of E. Some operational properties of representable effect algebras are established, and some applications of the obtained results are listed.     

Finite activation energy reactions Part 1: Reactants with spatially varying surface temperature

Summary The effect of a finite activation energy of reaction on the stability of reactants undergoing steady zero-order exothermic reactions is investigated. The reactants are exposed to a surface temperature which decreases slowly away from a global line maximum ofO(1). For both slab and cylinder geometries, it is found that large but finite activation energies can counteract the destabilising effect of the globalO(1) maximum in surface temperature.     

The variance of departure processes: puzzling behavior and open problems

We consider the variability of queueing departure processes. Previous results have shown the so-called BRAVO effect occurring in M/M/1/K and GI/G/1 queues: Balancing Reduces Asymptotic Variance of Outputs. A factor of (1?2/??) appears in GI/G/1 and a factor of 1/3 appears in M/M/1/K, for large K. A missing piece in the puzzle is the GI/G/1/K queue: Is there a BRAVO effect? If so, what is the variability? Does 1/3 play a role? This open problem paper addresses these questions by means of numeric and simulation results. We conjecture that at least for the case of light tailed distributions, the variability parameter is 1/3 multiplied by the sum of the squared coefficients of variations of the inter-arrival and service times.     

On the impact of model selection on predictor identification and parameter inference

We assessed the ability of several penalized regression methods for linear and logistic models to identify outcome-associated predictors and the impact of predictor selection on parameter inference for practical sample sizes. We studied effect estimates obtained directly from penalized methods (Algorithm 1), or by refitting selected predictors with standard regression (Algorithm 2). For linear models, penalized linear regression, elastic net, smoothly clipped absolute deviation (SCAD), least angle regression and LASSO had a low false negative (FN) predictor selection rates but false positive (FP) rates above 20 % for all sample and effect sizes. Partial least squares regression had few FPs but many FNs. Only relaxo had low FP and FN rates. For logistic models, LASSO and penalized logistic regression had many FPs and few FNs for all sample and effect sizes. SCAD and adaptive logistic regression had low or moderate FP rates but many FNs. 95 % confidence interval coverage of predictors with null effects was approximately 100 % for Algorithm 1 for all methods, and 95 % for Algorithm 2 for large sample and effect sizes. Coverage was low only for penalized partial least squares (linear regression). For outcome-associated predictors, coverage was close to 95 % for Algorithm 2 for large sample and effect sizes for all methods except penalized partial least squares and penalized logistic regression. Coverage was sub-nominal for Algorithm 1. In conclusion, many methods performed comparably, and while Algorithm 2 is preferred to Algorithm 1 for estimation, it yields valid inference only for large effect and sample sizes.     

A measure of bullwhip effect in supply chains with a mixed autoregressive-moving average demand process

In this paper, we quantify the impact of the bullwhip effect – the phenomenon in which information on demand is distorted as moving up a supply chain – for a simple two-stage supply chain with one supplier and one retailer. Assuming that the retailer employs a base stock inventory policy, and that the demand forecast is performed via a mixed autoregressive-moving average model, ARMA(1, 1), we investigate the effects of the autoregressive coefficient, the moving average parameter, and the lead time on the bullwhip effect.     

Tunneling planer Hall effect in Ni81Fe19/ Al2O3/NixFe1− x junction

Tunneling planer Hall (TPH) effect in Ni₈₁ Fe₁₉/Al₂O₃/Ni_xFe_1−x trilayer junction is different from general planer Hall effect in single-layer film or two-layer junction. This effect concerns the spin-polarized transport, so that the TPH voltage depends on the angle between magnetic vectors of two ferromagnetic layers. The TPH effect is reported to be influenced by composition and magnetic properties of FM layers and the thickness of the insulating layer.     

On the perron sign change effect for Lyapunov characteristic exponents of solutions of differential systems

The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with small second-order perturbations, which realizes only a partial Perron effect.     

Effect of scale and temperature factors on the compressive and shear strengths of plastics

Results are given of investigations of certain strength characteristics of a number of thermosetting plastics in relation to the scale of specimens reduced to 1/5 the standard size, i. e., the effect of the scale factor on the mechanical characteristics of plastics in compression and shear. In addition, results of a study of the dependence of the mechanical characteristics of plastics on the degree of heating in the temperature range from 20 to 200°C, i. e., the effect of the temperature factor on these characteristics, are also given.Mekhanika Polimerov, Vol. 1, No. 4, pp. 92–99, 1965     

Shorted operators of partitioned matrices and application

In this paper, our main objective is to study the effect of appending/deleting a column/row on the shorted operators. It turns out that for matrices A and B for which the shorted operator S(A|B) exists, S(A₁|B₁) of the matrix A₁=[A:a] with respect to the matrix B₁=[B:b], when it exists, is obtained by appending a suitable column to S(A|B). Moreover, if S(A₁|B₁) exists, then S(A|B) exists and is obtained from S(A₁|B₁) by dropping its last column. In the process, we study the effect of appending/deleting a column/row on the space pre-order and the parallel sum of parallel summable matrices. Finally, we specialize to the case of and matrices and study the effect of bordering (by an additional column and a row) on the shorted operator. We conclude the paper with an application to Linear Models with singular dispersion structure.     

Lingering issues in distributed scheduling

Recent advances have resulted in queue-based algorithms for medium access control which operate in a distributed fashion, and yet achieve the optimal throughput performance of centralized scheduling algorithms. However, fundamental performance bounds reveal that the “cautious” activation rules involved in establishing throughput optimality tend to produce extremely large delays, typically growing exponentially in $1/(1{-}\rho )$ , with $\rho $ the load of the system, in contrast to the usual linear growth. Motivated by that issue, we explore to what extent more “aggressive” schemes can improve the delay performance. Our main finding is that aggressive activation rules induce a lingering effect, where individual nodes retain possession of a shared resource for excessive lengths of time even while a majority of other nodes idle. Using central limit theorem type arguments, we prove that the idleness induced by the lingering effect may cause the delays to grow with $1/(1{-}\rho )$ at a quadratic rate. To the best of our knowledge, these are the first mathematical results illuminating the lingering effect and quantifying the performance impact. In addition extensive simulation experiments are conducted to illustrate and validate the various analytical results.     

Mathematical modeling and bifurcation analysis of pro- and anti-tumor macrophages

More and more evidences show that macrophages can induce both pro-tumor and anti-tumor effects. The study on genetically engineered macrophages to kill tumor cells has become a new direction for anti-cancer therapy in recent years. In this paper, we propose a mathematical model of interactions between tumor cells, M1 and M2 macrophages, and study the stability and bifurcations around the interior equilibrium. It is shown that the model exhibits stable periodic oscillations bifurcating from Hopf bifurcation, which indicates the long-term coexistence of tumor cells, M1 and M2 macrophages as well as long-term tumor relapse. Furthermore, sensitivity analysis is performed to illustrate the effect of parameters on tumor size. Our results show that an increase in ξ (the ratio of activation rates by tumor cells of M2/M1 macrophages) leads to a decrease of tumor cells, which can be explained that ξ has significant effects on γ₁ (the transition rate from M1 to M2 macrophages) and γ₂ (the transition rate from M2 to M1 macrophages). Hence, the decay of tumor cells is not only the result of direct activation of M1 and M2 macrophages by tumor cells, but also the combined effect of the transition between M1 and M2 macrophages.     

Raman scattering of nanocrystalline silicon embedded in SiO2

Raman scattering of nanocrystalline silicon embedded in SiO₂ matrix is systematically investigated. It is found that the Raman spectra can be well fitted by 5 Lorentzian lines in the Raman shift range of 100–600 cm⁻¹. The two-phonon scattering is also observed in the range of 600–1100 cm⁻¹. The experimental results indicate that the silicon crystallites in the films consist of nanocrystalline phase and amorphous phase; both can contribute to the Raman scattering. Besides the red-shift of the first order optical phonon modes with the decreasing size of silicon nanocrystallites, we have also found an enhancement effect on the second order Raman scattering, and the size effect on their Raman shift     

Effect of aspect ratio on the meridional circulation of a rotating homogeneous fluid

The effect of aspect ratio on the meridional circulation of a homogeneous fluid is analyzed. Aspect ratio is allowed to range between zero and unity. Relationships between possible horizontal and vertical length scales are obtained by length scale analysis as well as by solving an idealized problem. It is found that whenE ^1/2 ≪ Z ≪ E^1/2/δ, whereE is the Ekman number, the stream lines are closely packed near the sidewall within a thickness ofO(E ^1/2). The effect of stratification is unimportant within this depth range. In the depth rangeE ^1/2 /δ ≪ Z ≪ 1/Eδ the vertical boundary layer in which the streamlines are packed is ofO(EZδ) ^1/3. WhenZ ≫ 1/Eδ it is shown that the circulation decays algebraically with depth as 1/Z.     

Pointwise structure of a radiation hydrodynamic model in one-dimension

In this paper, we study the nonlinear stability and the pointwise structure around a constant equilibrium for a radiation hydrodynamic model in 1-dimension, in which the behavior of the fluid is described by a full Euler equation with certain radiation effect. It is well-known that the classical solutions of the Euler equation in 1-D may blow up in finite time for general initial data. The global existence of the solution in this paper means that the radiation effect stabilizes the system and prevents the formation of singularity when the initial data is small. To study the precise effect of the radiation in this model, we also treat the pointwise estimates of the solution for the original nonlinear problem by combining the Green's function for the linearized radiation hydrodynamic equations with the Duhamel's principle. The result in this paper shows that the pointwise structure of this model is similar to that of full Navier-Stokes equations in 1-D.     

Every effect algebra can be made into a total algebra

We prove that every effect algebra (E,+, 0, 1) can easily be made into a total algebra (E,⊕, ¬, 0) of type (2, 1, 0) in such a way that two elements are compatible in (E,+, 0, 1) if and only if they commute in (E,⊕, ¬, 0).     

Moduli spaces of 2-stage Postnikov systems

Using the obstruction theory of Blanc, Dwyer and Goerss, we compute the moduli space of realizations of 2-stage Π-algebras concentrated in dimensions 1 and n or in dimensions n and n+1. The main technical tools are Postnikov truncation and connected covers of Π-algebras, and their effect on Quillen cohomology.