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Статті в журналах з теми "J.T Bigge"
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Xia, Yonghui, and Jinde Cao. "ALMOST-PERIODIC SOLUTIONS FOR AN ECOLOGICAL MODEL WITH INFINITE DELAYS." Proceedings of the Edinburgh Mathematical Society 50, no. 1 (February 2007): 229–49. http://dx.doi.org/10.1017/s0013091504001233.
Повний текст джерелаАнотація:
AbstractBy using Lebesgue’s dominated convergence theorem and constructing a suitable Lyapunov functional, we study the following almost-periodic Lotka–Volterra model with $M$ predators and $N$ prey of the integro-differential equations\begin{alignat*}{2} \dot{x}_i(t)\amp=x_i(t)\biggl[b_i(t)-a_{ii}(t)x_i(t)-\sum_{k=1,k\neq i}^{N}a_{ik}(t)\int_{-\infty}^tH_{ik}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma\\ \amp\hskip45mm-\sum_{l=1}^{M}c_{il}(t)\int_{-\infty}^tK_{il}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad i\amp=1,2,\dots,N,\\ \dot{y}_j(t)\amp=y_j(t)\biggl[-r_j(t)-e_{jj}(t)y_j(t) +\sum_{k=1}^{N}d_{jk}(t)\int_{-\infty}^tP_{jk}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma \\ \amp\hskip45mm-\sum_{l=1,l\neq j}^{M} e_{jl}(t)\int_{-\infty}^tQ_{jl}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad j\amp=1,2,\dots,M. \end{alignat*}Some sufficient conditions are obtained for the existence of a unique almost-periodic solution of this model. Several examples show that the obtained criteria are new, general and easily verifiable.
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Gao, Fugen, and Meng Li. "Clarkson inequalities related to convex and concave functions." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1319–27. http://dx.doi.org/10.1515/ms-2021-0055.
Повний текст джерелаАнотація:
Abstract In this paper, we obtain some norm inequalities involving convex and concave functions, which are the generalizations of the classical Clarkson inequalities. Let A 1, …, A n be bounded linear operators on a complex separable Hilbert space H $\mathcal{H}$ and let α 1, …, α n be positive real numbers such that ∑ j = 1 n α j = 1 $\sum\limits^{n}_{j=1}\alpha_{j}=1$ . We show that for every unitarily invariant norm, If f is a non-negative function on [0, ∞) such that f(0) = 0 and g ( t ) = f ( t ) $g(t)=f(\sqrt{t})$ is convex, then | | | ∑ j = 1 n α j f ( | A j | ) | | | ≥ | | | ∑ j , k ∈ S ℓ ( f ( α j α k 4 α ℓ ( 1 − α ℓ ) | A j + A k − 2 ∑ j = 1 n α j A j | ) + f ( α j α k ( 2 α ℓ − 1 ) 4 α ℓ ( 1 − α ℓ ) | A j − A k | ) ) + f ( | ∑ j = 1 n α j A j | ) | | | $$\begin{align*} \bigg|\bigg|\bigg|\sum\limits^{n}_{j=1}\alpha_{j}f(|A_{j}|)\bigg|\bigg|\bigg| &\geq\bigg|\bigg|\bigg|\sum\limits_{j,k\in S_{\ell}}\bigg(f\bigg(\sqrt{\frac{\alpha_{j}\alpha_{k}}{4\alpha_{\ell}(1-\alpha_{\ell})}}\;\bigg|A_{j}+A_{k}-2\sum\limits^{n}_{j=1}\alpha_{j}A_{j}\bigg|\bigg)\\ &\qquad+f\bigg(\sqrt{\frac{\alpha_{j}\alpha_{k}(2\alpha_{\ell}-1)}{4\alpha_{\ell}(1-\alpha_{\ell})}}|A_{j}-A_{k}|\bigg)\bigg)+f\bigg(\bigg|\sum\limits^{n}_{j=1}\alpha_{j}A_{j}\bigg|\bigg)\bigg|\bigg|\bigg| \end{align*}$$ for ℓ = 1, …, n. If f is a non-negative function on [0, ∞) such that g ( t ) = f ( t ) $g(t)=f(\sqrt{t})$ is concave, then the inverse inequality holds. Here, the symbol S ℓ = {1, …, n} ∖ {ℓ} for ℓ ∈ {1, …, n}. In addition, we provide some applications of the above inequalities.
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El-Sheikh, Mohamed M. A., Ragaa Sallam, and Shaimaa Salem. "Oscillation of nonlinear third-order differential equations with several sublinear neutral terms." Mathematica Slovaca 71, no. 6 (December 1, 2021): 1411–26. http://dx.doi.org/10.1515/ms-2021-0061.
Повний текст джерелаАнотація:
Abstract A class of third order differential equations with several sublinear neutral terms of the type ( a ( t ) ( b ( t ) ( x ( t ) + ∑ j = 1 n p j ( t ) x α j ( τ j ( t ) ) ) ′ ) ′ ) ′ + ∑ i = 1 m f i ( t , x ( σ i ( t ) ) ) = 0 , t ≥ t 0 > 0 $$\begin{array}{} \displaystyle \bigg( a(t)\Big( b(t)\Big(x(t)+\sum\limits_{j=1}^{n}p_{j}(t)x^{\alpha _{j}}(\tau _{j}(t))\Big)'\Big)'\bigg)' +\sum\limits_{i=1}^{m}f_{i}(t,x(\sigma _{i}(t)))=0,\qquad t\geq t_{0} \gt 0 \end{array}$$ is considered. Some oscillation criteria are presented to improve and complement those in the literature. Two examples are established to illustrate the main results.
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Jebelean, Petru, Jean Mawhin, and Călin Şerban. "Morse theory and multiple periodic solutions of some quasilinear difference systems with periodic nonlinearities." Georgian Mathematical Journal 24, no. 1 (March 1, 2017): 103–12. http://dx.doi.org/10.1515/gmj-2016-0075.
Повний текст джерелаАнотація:
AbstractWe consider the system of difference equations$\Delta\bigg{(}\frac{\Delta u_{n-1}}{\sqrt{1-|\Delta u_{n-1}|^{2}}}\bigg{)}=% \nabla V_{n}(u_{n})+h_{n},\quad u_{n}=u_{n+T}\quad(n\in\mathbb{Z}),$with${\Delta u_{n}=u_{n+1}-u_{n}\in{\mathbb{R}}^{N}}$,${V_{n}=V_{n}(x)\in C^{2}({\mathbb{R}}^{N},\mathbb{R})}$,${V_{n+T}=V_{n}}$,${h_{n+T}=h_{n}}$for all${n\in\mathbb{Z}}$and some positive integerT,${V_{n}(x)}$is${\omega_{i}}$-periodic (${\omega_{i}>0}$) with respect to each${x_{i}}$(${i=1,\ldots,N}$) and${\sum_{j=1}^{T}h_{j}=0}$. Applying a modification argument to the corresponding problem with a left-hand member ofp-Laplacian type, and using Morse theory, we prove that if all its solutions are non-degenerate, then the difference system above has at least${2^{N}}$geometrically distinctT-periodic solutions.
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Rademacher, Markus, James Millen, and Ying Lia Li. "Quantum sensing with nanoparticles for gravimetry: when bigger is better." Advanced Optical Technologies 9, no. 5 (November 26, 2020): 227–39. http://dx.doi.org/10.1515/aot-2020-0019.
Повний текст джерелаАнотація:
AbstractFollowing the first demonstration of a levitated nanosphere cooled to the quantum ground state in 2020 (U. Delić, et al. Science, vol. 367, p. 892, 2020), macroscopic quantum sensors are seemingly on the horizon. The nanosphere’s large mass as compared to other quantum systems enhances the susceptibility of the nanoparticle to gravitational and inertial forces. In this viewpoint, we describe the features of experiments with optically levitated nanoparticles (J. Millen, T. S. Monteiro, R. Pettit, and A. N. Vamivakas, “Optomechanics with levitated particles,” Rep. Prog. Phys., vol. 83, 2020, Art no. 026401) and their proposed utility for acceleration sensing. Unique to the levitated nanoparticle platform is the ability to implement not only quantum noise limited transduction, predicted by quantum metrology to reach sensitivities on the order of 10−15 ms−2 (S. Qvarfort, A. Serafini, P. F. Barker, and S. Bose, “Gravimetry through non-linear optomechanics,” Nat. Commun., vol. 9, 2018, Art no. 3690) but also long-lived quantum spatial superpositions for enhanced gravimetry. This follows a global trend in developing sensors, such as cold-atom interferometers, that exploit superposition or entanglement. Thanks to significant commercial development of these existing quantum technologies, we discuss the feasibility of translating levitated nanoparticle research into applications.
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Xuan, Ziming, Jason G. Blanchette, Toben F. Nelson, Timothy C. Heeren, Thien H. Nguyen, and Timothy S. Naimi. "Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies." International Journal of Alcohol and Drug Research 4, no. 2 (December 18, 2015): 119–30. http://dx.doi.org/10.7895/ijadr.v2i0.205.
Повний текст джерелаАнотація:
Xuan, Z., Blanchette, J., Nelson, T., Heeren, T., Nguyen, T., & Naimi, T. (2015). Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies. The International Journal Of Alcohol And Drug Research, 4(2), 119-130. doi:http://dx.doi.org/10.7895/ijadr.v4i2.205Aims: To test the hypotheses that stronger policy environments are associated with less impaired driving and that driving-orientedand drinking-oriented policy subgroups are independently associated with impaired driving.Design: State-level data on 29 policies in 50 states from 2001-2009 were used as lagged exposures in generalized linearregression models to predict self-reported impaired driving.Setting: Fifty United States and Washington, D.C.Participants: A total of 1,292,245 adults (≥ 18 years old) biennially from 2002–2010.Measures: Alcohol Policy Scale scores representing the alcohol policy environment were created by summing policies weightedby their efficacy and degree of implementation by state-year. Past-30-day alcohol-impaired driving from 2002–2010 wasobtained from the Behavioral Risk Factor Surveillance System surveys.Findings: Higher Alcohol Policy Scale scores are strongly associated with lower state-level prevalence and individual-level risk of impaired driving. After accounting for driving-oriented policies, drinking-oriented policies had a robust independent association with reduced likelihood of impaired driving. Reduced binge drinking mediates the relationship between drinking-oriented policies and impaired driving, and driving-oriented policies reduce the likelihood of impaired driving among binge drinkers.Conclusions: Efforts to reduce alcohol-impaired driving should focus on reducing excessive drinking in addition to preventing driving among those who are impaired.
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Xuan, Ziming, Jason G. Blanchette, Toben F. Nelson, Timothy C. Heeren, Thien H. Nguyen, and Timothy S. Naimi. "Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies." International Journal of Alcohol and Drug Research 4, no. 2 (December 18, 2015): 119–30. http://dx.doi.org/10.7895/ijadr.v4i2.205.
Повний текст джерелаАнотація:
Xuan, Z., Blanchette, J., Nelson, T., Heeren, T., Nguyen, T., & Naimi, T. (2015). Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies. The International Journal Of Alcohol And Drug Research, 4(2), 119-130. doi:http://dx.doi.org/10.7895/ijadr.v4i2.205Aims: To test the hypotheses that stronger policy environments are associated with less impaired driving and that driving-orientedand drinking-oriented policy subgroups are independently associated with impaired driving.Design: State-level data on 29 policies in 50 states from 2001-2009 were used as lagged exposures in generalized linearregression models to predict self-reported impaired driving.Setting: Fifty United States and Washington, D.C.Participants: A total of 1,292,245 adults (≥ 18 years old) biennially from 2002–2010.Measures: Alcohol Policy Scale scores representing the alcohol policy environment were created by summing policies weightedby their efficacy and degree of implementation by state-year. Past-30-day alcohol-impaired driving from 2002–2010 wasobtained from the Behavioral Risk Factor Surveillance System surveys.Findings: Higher Alcohol Policy Scale scores are strongly associated with lower state-level prevalence and individual-level risk of impaired driving. After accounting for driving-oriented policies, drinking-oriented policies had a robust independent association with reduced likelihood of impaired driving. Reduced binge drinking mediates the relationship between drinking-oriented policies and impaired driving, and driving-oriented policies reduce the likelihood of impaired driving among binge drinkers.Conclusions: Efforts to reduce alcohol-impaired driving should focus on reducing excessive drinking in addition to preventing driving among those who are impaired.
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Xuan, Ziming, Jason G. Blanchette, Toben F. Nelson, Timothy C. Heeren, Thien H. Nguyen, and Timothy S. Naimi. "Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies." International Journal of Alcohol and Drug Research 4, no. 2 (December 18, 2015): 119–30. http://dx.doi.org/10.7895/ijadr.v4i2.205aims.
Повний текст джерелаАнотація:
Xuan, Z., Blanchette, J., Nelson, T., Heeren, T., Nguyen, T., & Naimi, T. (2015). Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies. The International Journal Of Alcohol And Drug Research, 4(2), 119-130. doi:http://dx.doi.org/10.7895/ijadr.v4i2.205Aims: To test the hypotheses that stronger policy environments are associated with less impaired driving and that driving-orientedand drinking-oriented policy subgroups are independently associated with impaired driving.Design: State-level data on 29 policies in 50 states from 2001-2009 were used as lagged exposures in generalized linearregression models to predict self-reported impaired driving.Setting: Fifty United States and Washington, D.C.Participants: A total of 1,292,245 adults (≥ 18 years old) biennially from 2002–2010.Measures: Alcohol Policy Scale scores representing the alcohol policy environment were created by summing policies weightedby their efficacy and degree of implementation by state-year. Past-30-day alcohol-impaired driving from 2002–2010 wasobtained from the Behavioral Risk Factor Surveillance System surveys.Findings: Higher Alcohol Policy Scale scores are strongly associated with lower state-level prevalence and individual-level risk of impaired driving. After accounting for driving-oriented policies, drinking-oriented policies had a robust independent association with reduced likelihood of impaired driving. Reduced binge drinking mediates the relationship between drinking-oriented policies and impaired driving, and driving-oriented policies reduce the likelihood of impaired driving among binge drinkers.Conclusions: Efforts to reduce alcohol-impaired driving should focus on reducing excessive drinking in addition to preventing driving among those who are impaired.
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Xuan, Ziming, Jason G. Blanchette, Toben F. Nelson, Timothy C. Heeren, Thien H. Nguyen, and Timothy S. Naimi. "Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies." International Journal of Alcohol and Drug Research 4, no. 2 (December 18, 2015): 119–30. http://dx.doi.org/10.7895/ijadr.vxiy.205.
Повний текст джерелаАнотація:
Xuan, Z., Blanchette, J., Nelson, T., Heeren, T., Nguyen, T., & Naimi, T. (2015). Alcohol policies and impaired driving in the United States: Effects of driving- vs. drinking-oriented policies. The International Journal Of Alcohol And Drug Research, 4(2), 119-130. doi:http://dx.doi.org/10.7895/ijadr.v4i2.205Aims: To test the hypotheses that stronger policy environments are associated with less impaired driving and that driving-orientedand drinking-oriented policy subgroups are independently associated with impaired driving.Design: State-level data on 29 policies in 50 states from 2001-2009 were used as lagged exposures in generalized linearregression models to predict self-reported impaired driving.Setting: Fifty United States and Washington, D.C.Participants: A total of 1,292,245 adults (≥ 18 years old) biennially from 2002–2010.Measures: Alcohol Policy Scale scores representing the alcohol policy environment were created by summing policies weightedby their efficacy and degree of implementation by state-year. Past-30-day alcohol-impaired driving from 2002–2010 wasobtained from the Behavioral Risk Factor Surveillance System surveys.Findings: Higher Alcohol Policy Scale scores are strongly associated with lower state-level prevalence and individual-level risk of impaired driving. After accounting for driving-oriented policies, drinking-oriented policies had a robust independent association with reduced likelihood of impaired driving. Reduced binge drinking mediates the relationship between drinking-oriented policies and impaired driving, and driving-oriented policies reduce the likelihood of impaired driving among binge drinkers.Conclusions: Efforts to reduce alcohol-impaired driving should focus on reducing excessive drinking in addition to preventing driving among those who are impaired.
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Jagan, Kavya, and Alistair B. Forbes. "Assessing interlaboratory comparison data adjustment procedures." International Journal of Metrology and Quality Engineering 10 (2019): 3. http://dx.doi.org/10.1051/ijmqe/2019003.
Повний текст джерелаАнотація:
Interlaboratory comparisons (ILCs) are one of the key activities in metrology. Estimates x = (x1,…, xn) T of a measurand α along with their associated standard uncertainties u0 = (u0,1,…, u0,n) T, u0,j = u0 (xj) are provided by each of n laboratories. Employing a model of the form xj ∈ N(α, v0,j), j = 1,…,n, v0,j = u0,j2, we may wish to find a consensus value for α. A χ2 test can be used to assess the degree to which the spread of the estimates x are consistent with the stated uncertainties u0. If they are judged to be inconsistent, then an adjustment procedure can be applied to determine vj ≥ v0,j, so that x and v represent consistency. The underlying assumption behind this approach is that some or all of the laboratories have underestimated or neglected some uncertainty contributions, sometimes referred to as ‘dark uncertainty’, and the adjusted v provides an estimate of this dark uncertainty derived from the complete set of laboratory results. There are many such adjustment procedures, including the Birge and Mandel–Paule (M-P) procedures. In implementing an adjustment procedure, a desirable objective is to make as minimal an adjustment as necessary in order to bring about the required degree of consistency. In this paper, we discuss the use of relative entropy, also known as the Kullback–Leibler divergence, as a measure of the degree of adjustment. We consider parameterising v = v (b) as a function of parameters b with the input v0 = v (b0) for some b0. We look to perturb b from b0 to bring about consistency in a way that minimises how far b is from b0 in terms of the relative entropy or Kullback–Leibler divergence.