Journal articles: 'Extremal range'

1

Bingham, N. H. "The sample mid-range and symmetrized extremal laws." Statistics & Probability Letters 23, no. 3 (May 1995): 281–88. http://dx.doi.org/10.1016/0167-7152(94)00126-s.

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Samorodnitsky, Gennady, and Yizao Wang. "Extremal theory for long range dependent infinitely divisible processes." Annals of Probability 47, no. 4 (July 2019): 2529–62. http://dx.doi.org/10.1214/18-aop1318.

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Croydon, David A., Ryoki Fukushima, and Stefan Junk. "Extremal regime for one-dimensional Mott variable-range hopping." Annales Henri Lebesgue 6 (December 12, 2023): 1169–211. http://dx.doi.org/10.5802/ahl.186.

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Barakat, H. M., E. M. Nigm, and A. M. Elsawah. "Asymptotic Distributions of the Generalized Range, Midrange, Extremal Quotient, and Extremal Product, with a Comparison Study." Communications in Statistics - Theory and Methods 44, no. 5 (March 3, 2015): 900–913. http://dx.doi.org/10.1080/03610926.2012.750356.

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Alokley, Sara Ali, and Mansour Saleh Albarrak. "Clustering of Extremes in Financial Returns: A Study of Developed and Emerging Markets." Journal of Risk and Financial Management 13, no. 7 (July 2, 2020): 141. http://dx.doi.org/10.3390/jrfm13070141.

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This paper investigates the clustering or dependency of extremes in financial returns by estimating the extremal index value, in which smaller values of the extremal index correspond to more clustering. We apply the interval estimator method to determine the extremal index for a range of threshold values in the developed and emerging markets from 2007–2017. The indices we used to represent developed markets are from France, Germany, Italy, Japan, USA, UK, Spain, and Sweden. For the emerging markets, we use indices from China, Brazil, India, Malaysia, Russia, Saudi Arabia, and Portugal. The results show that clustering occurs in the emerging and developed markets under several threshold values. This study will shed light on the dependency structure of financial returns data and the proprieties of the extremes returns. Moreover, understanding clustering of extremes in these markets can help investors reduce the exposure to extreme financial events, such as the financial crisis.

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Crabb, M. J., J. Duncan, and C. M. McGregor. "Some extremal algebras for hermitians." Glasgow Mathematical Journal 43, no. 1 (January 2001): 29–38. http://dx.doi.org/10.1017/s0017089501010047.

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We study three extremal Banach algebras: (a) generated by two hermitian unitaries; (b) generated by an element of norm 1 all of whose odd positive powers are hermitian; (c) generated by an element of norm 1 all of whose even positive powers are hermitian. In all three cases the numerical range is found for various elements. The second algebra is shown to be isometrically isomorphic to a subalgebra of the first. The third algebra is identified with a space of functions.

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Chen, Zaoli, and Gennady Samorodnitsky. "Extremal clustering under moderate long range dependence and moderately heavy tails." Stochastic Processes and their Applications 145 (March 2022): 86–116. http://dx.doi.org/10.1016/j.spa.2021.12.001.

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Masumoto, Makoto. "Extremal lengths of homology classes on Riemann surfaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 508 (March 12, 1999): 17–45. http://dx.doi.org/10.1515/crll.1999.508.17.

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Abstract We assign a positive number V, a new conformal invariant, to a Riemann surface R of finite genus in terms of the extremal lengths of certain weak homology classes on R, and determine the range of V. In particular we find algebraic relations among the extremal lengths of homology classes on compact Riemann surfaces.

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Fasen, Vicky. "Extremes of regularly varying Lévy-driven mixed moving average processes." Advances in Applied Probability 37, no. 04 (December 2005): 993–1014. http://dx.doi.org/10.1017/s000186780000063x.

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In this paper, we study the extremal behavior of stationary mixed moving average processes of the formY(t)=∫ℝ+×ℝf(r,t-s) dΛ(r,s),t∈ℝ, wherefis a deterministic function and Λ is an infinitely divisible, independently scattered random measure whose underlying driving Lévy process is regularly varying. We give sufficient conditions for the stationarity ofYand compute the tail behavior of certain functionals ofY. The extremal behavior is modeled by marked point processes on a discrete-time skeleton chosen properly by the jump times of the underlying driving Lévy process and the extremes of the kernel function. The sequences of marked point processes converge weakly to a cluster Poisson random measure and reflect extremes ofYat a high level. We also show convergence of the partial maxima to the Fréchet distribution. Our models and results cover short- and long-range dependence regimes.

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Carlson, David, and Charles R. Johnson. "Extremal patterns of distinct entries in vectors in the range of a matrix." Linear and Multilinear Algebra 43, no. 1-3 (January 1997): 283–97. http://dx.doi.org/10.1080/03081089708818529.

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Arutyunov, A. V. "Second-order conditions in extremal problems with finite-dimensional range. 2-normal maps." Izvestiya: Mathematics 60, no. 1 (February 28, 1996): 39–65. http://dx.doi.org/10.1070/im1996v060n01abeh000061.

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Fasen, Vicky. "Extremes of regularly varying Lévy-driven mixed moving average processes." Advances in Applied Probability 37, no. 4 (December 2005): 993–1014. http://dx.doi.org/10.1239/aap/1134587750.

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In this paper, we study the extremal behavior of stationary mixed moving average processes of the form Y(t)=∫ℝ+×ℝf(r,t-s) dΛ(r,s), t∈ℝ, where f is a deterministic function and Λ is an infinitely divisible, independently scattered random measure whose underlying driving Lévy process is regularly varying. We give sufficient conditions for the stationarity of Y and compute the tail behavior of certain functionals of Y. The extremal behavior is modeled by marked point processes on a discrete-time skeleton chosen properly by the jump times of the underlying driving Lévy process and the extremes of the kernel function. The sequences of marked point processes converge weakly to a cluster Poisson random measure and reflect extremes of Y at a high level. We also show convergence of the partial maxima to the Fréchet distribution. Our models and results cover short- and long-range dependence regimes.

13

Mhaskar, H. N. "Finite-infinite range inequalities in the complex plane." International Journal of Mathematics and Mathematical Sciences 14, no. 4 (1991): 625–38. http://dx.doi.org/10.1155/s0161171291000868.

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LetE⫅Cbe closed,ωbe a suitable weight function onE,σbe a positive Borel measure onE. We discuss the conditions onωandσwhich ensure the existence of a fixed compact subsetKofEwith the following property. For anyp,0<P≤∞, there exist positive constantsc1, c2depending only onE,ω,σandpsuch that for every integern≥1and every polynomialPof degree at mostn,∫E\K|ωnP|pdσ≤c1exp(−c2n)∫K|ωnP|pdσ. In particular, we shall show that the support of a certain extremal measure is, in some sense, the smallest setKwhich works. The conditions onσare formulated in terms of certain localized Christoffel functions related toσ.

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Le Gruyer, Erwan Y. "Extremal extension for m-jets of one variable with range in a Hilbert space." Advances in Mathematics 281 (August 2015): 1274–84. http://dx.doi.org/10.1016/j.aim.2015.06.009.

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Bianchini, Stefano. "Extremal Faces of the Range of a Vector Measure and a Theorem of Lyapunov." Journal of Mathematical Analysis and Applications 231, no. 1 (March 1999): 301–18. http://dx.doi.org/10.1006/jmaa.1998.6260.

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Barakat, Haroon M., and M. A. Abd Elgawad. "Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications." Mathematica Slovaca 69, no. 3 (June 26, 2019): 707–20. http://dx.doi.org/10.1515/ms-2017-0259.

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Abstract In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df’s) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

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Chernogorov, Ivan, Victor Polyakh, and Orkhan Yarakhmedov. "Search Optimization Opportunities of Modified Self-Organizing Migrating Algorithm in Multi-Extremal Tasks Environment." Journal of Advanced Engineering and Computation 1, no. 2 (November 30, 2017): 144. http://dx.doi.org/10.25073/jaec.201712.60.

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The paper studies the search optimization task of multi-extremal objects, which are more complicated than mono-extremal. Paper postulates that to find extreme suitable values on complex test function the heuristic algorithm is one way. Self-Organizing Migrating Algorithm and devised approach applied to this task are considered. Conducted research established common test environment to compare multi-extremal test functions. Specific characteristics for problem solving of detection and identification of global and local extreme are included. Additional clustering mechanism are described. Obtained measurements and computing times of Self-Organizing Migrating Algorithm on a range of multi-extremal test functions are illustrated. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

18

Yue, Yuan, and Yong-Qiang Wang. "Excited States of Maximal Warm Holes." Universe 9, no. 7 (July 19, 2023): 338. http://dx.doi.org/10.3390/universe9070338.

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Recently, the Einstein–Maxwell–scalar model with a non-minimal coupling between the scalar and Maxwell fields was explored. As a result, a new class of black hole solutions with scalar hair was discovered. By fixing the mass of a black hole and taking the maximum allowable charge, an extremal black hole was obtained. Interestingly, this extremal black hole not only possesses an event horizon with a non-zero surface area but also exhibits a non-zero Hawking temperature. This unique type of extremal black hole is referred to as a maximal warm hole (MWH). In this paper, we revisit this model and examine these black holes with highly excited state fields. We discovered that an excited state MWH solution can also be obtained under extremal conditions. We investigate the range of existence for excited states and analyze their relevant physical properties.

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Ledford, Anthony W., and Jonathan A. Tawn. "Concomitant tail behaviour for extremes." Advances in Applied Probability 30, no. 1 (March 1998): 197–215. http://dx.doi.org/10.1239/aap/1035228000.

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The influence of bivariate extremal dependence on the limiting behaviour of the concomitant of the largest order statistic is examined. Our approach is to fix the marginal distributions and derive a general tail characterisation of the joint survivor function. From this, we identify the normalisation required to obtain the limiting distribution of the concomitant of the largest order statistic, obtain its tail form, and investigate the limiting probability that the vector of componentwise maxima occurs as an observation of the bivariate process. The results are illustrated for a range of extremal dependence forms.

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Ledford, Anthony W., and Jonathan A. Tawn. "Concomitant tail behaviour for extremes." Advances in Applied Probability 30, no. 01 (March 1998): 197–215. http://dx.doi.org/10.1017/s0001867800008168.

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The influence of bivariate extremal dependence on the limiting behaviour of the concomitant of the largest order statistic is examined. Our approach is to fix the marginal distributions and derive a general tail characterisation of the joint survivor function. From this, we identify the normalisation required to obtain the limiting distribution of the concomitant of the largest order statistic, obtain its tail form, and investigate the limiting probability that the vector of componentwise maxima occurs as an observation of the bivariate process. The results are illustrated for a range of extremal dependence forms.

21

Hürlimann, Werner. "Improved Analytical Bounds for Some Risk Quantities." ASTIN Bulletin 26, no. 2 (November 1996): 185–99. http://dx.doi.org/10.2143/ast.26.2.563218.

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AbstractSimple analytical lower and upper bounds are obtained for stop-loss premiums and ruin probabilities of compound Poisson risks in case the mean, variance and range of the claim size distribution are known. They are based on stop-loss extremal distributions and improve the bounds derived earlier from dangerous extremal distributions. The special bounds obtained in case the relative variance of the claim size is unknown, but its maximal value is known, are related to other actuarial results.

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Resnick, Sidney, and Rishin Roy. "Multivariate extremal processes, leader processes and dynamic choice models." Advances in Applied Probability 22, no. 2 (June 1990): 309–31. http://dx.doi.org/10.2307/1427538.

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Let (Y(t), t > 0) be a d-dimensional non-homogeneous multivariate extremal process. We suppose the ith component of Y describes time-dependent behaviour of random utilities associated with the ith choice. At time t we choose the ith alternative if the ith component of Y(t) is the largest of all the components. Let J(t) be the index of the largest component at time t so J has range {1, …, d} and call {J(t)} the leader process. Let Z(t) be the value of the largest component at time t. Then the bivariate process (J(t), Z(t)} is Markov. We discuss when J(t) and Z(t) are independent, when {J(s), 0<s≦t} and Z(t) are independent and when J(t) and {Z(s), 0<s≦t} are independent. In usual circumstances, {J(t)} is Markov and particular properties are given when the underlying distribution is max-stable. In the max-stable time-homogeneous case, {J(et)} is a stationary Markov chain with stationary transition probabilities.

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Resnick, Sidney, and Rishin Roy. "Multivariate extremal processes, leader processes and dynamic choice models." Advances in Applied Probability 22, no. 02 (June 1990): 309–31. http://dx.doi.org/10.1017/s0001867800019595.

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Let ( Y (t), t > 0) be a d-dimensional non-homogeneous multivariate extremal process. We suppose the ith component of Y describes time-dependent behaviour of random utilities associated with the ith choice. At time t we choose the ith alternative if the ith component of Y (t) is the largest of all the components. Let J(t) be the index of the largest component at time t so J has range {1, …, d} and call {J(t)} the leader process. Let Z(t) be the value of the largest component at time t. Then the bivariate process (J(t), Z(t)} is Markov. We discuss when J(t) and Z(t) are independent, when {J(s), 0<s≦t} and Z(t) are independent and when J(t) and {Z(s), 0<s≦t} are independent. In usual circumstances, {J(t)} is Markov and particular properties are given when the underlying distribution is max-stable. In the max-stable time-homogeneous case, {J(et )} is a stationary Markov chain with stationary transition probabilities.

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Dimitrijevic-Ciric, Marija, Nikola Konjik, and Andjelo Samsarov. "Scalar quasinormal modes of the near extremal Reissner-Nordström black hole in NC space-time." Facta universitatis - series: Physics, Chemistry and Technology 17, no. 1, spec.issue (2019): 43–51. http://dx.doi.org/10.2298/fupct1901043d.

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A way to search for a signal of space-time noncommutativity is to study a quasinormal mode spectrum of the Reissner-Nordstr?m black hole in the presence of noncommutativity. In this paper, we chose a particular NC deformation defined by the angular twist. We investigate a noncommutative (NC) deformation of a complex scalar field, minimally coupled with a classical (commutative) near extremal Reissner-Nordstr?m background. The theory is manifestly invariant under the deformed U(1)* gauge symmetry group. Using the EOM for the NC complex scalar field in RN background, the QNM spectrum is calculated for a particular range of parameters coresponding to the near extremal limit.

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Bellucci, Stefano, and Bhupendra Nath Tiwari. "State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory." Advances in High Energy Physics 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/589031.

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We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.

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Johnson, Lane R., and Richard C. Lee. "Extremal bounds on the P velocity in the Earth's core." Bulletin of the Seismological Society of America 75, no. 1 (February 1, 1985): 115–30. http://dx.doi.org/10.1785/bssa0750010115.

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Abstract Global travel-time data from the ISC Bulletin were used to determine the function τ(p) for core phases. Estimates were obtained for the AB, BC, DE, and EF branches of the PKP phase and also for the SKS and SKKS phases. The data were all analyzed in a uniform manner to yield 31 estimates of τ(p) and its uncertainty at the 99.9 per cent confidence level in a range of p which covers most of the core. The effects of the mantle were removed with the PREM velocity models. The extremal bounds on the P velocity in the core were estimated at the joint confidence level of 97 per cent. The average width of the velocity bounds is about 0.6 km/sec, with the major source of uncertainty coming from the SKS and SKKS data. The outer core-inner core transition zone is well constrained, and the results favor a simple fairly abrupt increase in velocity.

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Mikuła, Jarosław, Daniel Pakuła, Ludwina Żukowska, Klaudiusz Gołombek, and Antonín Kříž. "Wear Resistance of (Ti,Al)N Metallic Coatings for Extremal Working Conditions." Coatings 11, no. 2 (January 29, 2021): 157. http://dx.doi.org/10.3390/coatings11020157.

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The article includes research results for the functional properties achieved for a wide range of sintered tool materials, including sintered carbides, cermets and three types of Al2O3 oxide tool ceramics ((Al2O3 + ZrO2, Al2O3 + TiC and Al2O3 + SiC(w)) with (Ti,Al)N coating deposited in the cathodic arc evaporation (CAE-PVD) method and comparison with uncoated tool materials. For all coated samples, a uniform wear pattern on tool shank was observed during metallographic analysis. Based on the scanning electron microscope (SEM) metallographic analysis, it was found that the most common types of tribological defects identified in tested materials are: mechanical defects and abrasive wear of the tool side, crater formation on the tool face, cracks on the tool side, chipping on the cutting edge and built-up edge from chip fragments. Deposition of (Ti,Al)N coating on all tested substrates increases the wear resistance and also limits the exceeding of critical levels of permanent stresses. It even increases the tool life many times over. Such a significant increase in tool life results, among other things, from a large increase in microhardness of PVD coated materials compared to uncoated samples, increased resistance to thermal and chemical abrasion, improved chip formation and removal process conditions. Use of hard coatings applied to sintered tool materials is considered to be one of the most important achievements in improving the functional properties of cutting tools and can still be developed by improving the coating structure solutions (sorted and nanocrystalline structures) and extending the range of coating applications (Ti,Al)N in a variety of substrates.

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Mossige, Svein. "The Postage Stamp Problem: An algorithm to determine the $h$-range on the $h$-range formula on the extremal basis problem for $k=4$." Mathematics of Computation 69, no. 229 (August 23, 1999): 325–38. http://dx.doi.org/10.1090/s0025-5718-99-01204-1.

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Elek, P., and L. Márkus. "A long range dependent model with nonlinear innovations for simulating daily river flows." Natural Hazards and Earth System Sciences 4, no. 2 (April 16, 2004): 277–83. http://dx.doi.org/10.5194/nhess-4-277-2004.

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Abstract. We present the analysis aimed at the estimation of flood risks of Tisza River in Hungary on the basis of daily river discharge data registered in the last 100 years. The deseasonalised series has skewed and leptokurtic distribution and various methods suggest that it possesses substantial long memory. This motivates the attempt to fit a fractional ARIMA model with non-Gaussian innovations as a first step. Synthetic streamflow series can then be generated from the bootstrapped innovations. However, there remains a significant difference between the empirical and the synthetic density functions as well as the quantiles. This brings attention to the fact that the innovations are not independent, both their squares and absolute values are autocorrelated. Furthermore, the innovations display non-seasonal periods of high and low variances. This behaviour is characteristic to generalised autoregressive conditional heteroscedastic (GARCH) models. However, when innovations are simulated as GARCH processes, the quantiles and extremes of the discharge series are heavily overestimated. Therefore we suggest to fit a smooth transition GARCH-process to the innovations. In a standard GARCH model the dependence of the variance on the lagged innovation is quadratic whereas in our proposed model it is a bounded function. While preserving long memory and eliminating the correlation from both the generating noise and from its square, the new model is superior to the previously mentioned ones in approximating the probability density, the high quantiles and the extremal behaviour of the empirical river flows.

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Wu, Bin, Weiyang Liu, Hao Tang, and Rui-Hong Yue. "Destroying charged black holes in higher dimensions with test particles." International Journal of Modern Physics A 32, no. 21 (July 30, 2017): 1750125. http://dx.doi.org/10.1142/s0217751x17501251.

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A possible way to destroy the Tangherlini Reissner–Nordström black hole is discussed in the spirit of Wald’s gedanken experiment. By neglecting radiation and self force effects, the absorbing condition and destruction condition of the test point particle which is capable of destroying the black hole are obtained. We find that it is impossible to challenge the weak cosmic censorship for an initially extremal black hole in all dimensions. Instead, it is shown that the near extremal black hole will turn into a naked singularity in this particular process, in which case the allowed range of the particle’s energy is very narrow. The result indicates that the self-force effects may well change the outcome of the calculation.

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MESHOUL, SOUHAM, and MOHAMED BATOUCHE. "COMBINING EXTREMAL OPTIMIZATION WITH SINGULAR VALUE DECOMPOSITION FOR EFFECTIVE POINT MATCHING." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 07 (November 2003): 1111–26. http://dx.doi.org/10.1142/s0218001403002782.

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Feature point matching is a key step for most problems in computer vision. It is an ill-posed problem and suffers from combinatorial complexity which becomes even more critical with the increase in data and the presence of outliers. The work covered in this paper describes a new framework to solve this problem in order to achieve robust registration of two feature point sets assumed to be available. This framework combines the use of extremal optimization heuristic with a clever startup routine which exploits some properties of singular value decomposition. The role of the latter is to produce an interesting matching configuration whereas the role of the former is to refine the initial matching by generating hypothetical matches and outliers using a far-from-equilibrium based stochastic rule. Experiments on a wide range of real data have shown the effectiveness of the proposed method and its ability to achieve reliable feature point matching.

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Dissanayake, Pushpa, Teresa Flock, Johanna Meier, and Philipp Sibbertsen. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights." Mathematics 9, no. 21 (November 5, 2021): 2817. http://dx.doi.org/10.3390/math9212817.

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The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification.

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Kaftal, Victor, Ping Wong Ng, and Shuang Zhang. "Strict Comparison of Positive Elements in Multiplier Algebras." Canadian Journal of Mathematics 69, no. 02 (April 2017): 373–407. http://dx.doi.org/10.4153/cjm-2016-015-3.

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AbstractMain result: If a C*-algebrais simple,σ-unital, hasfinitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier algebraalso has strict comparison of positive elements by traces. The same results holds if finitely many extremal traces is replaced byquasicontinuous scale. A key ingredient in the proof is that every positive element in the multiplier algebra of an arbitrary σ-unital C* -algebra can be approximated by a bi-diagonal series. As an application of strict comparison, ifis a simple separable stable C* -algebra with real rank zero, stable rank one, and strict comparison of positive elements by traces, then whether a positive element is a positive linear combination of projections is determined by the trace values of its range projection.

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Guioth, Jules, and Robert L. Jack. "Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 10 (October 1, 2021): 103206. http://dx.doi.org/10.1088/1742-5468/ac2895.

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Abstract We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range of dynamical phase transitions, including spontaneous symmetry breaking into ordered states. For weak bias, the phase behaviour is controlled by extrema of the free energy, which may be local minima or saddle points. For large bias, the system tends to states of extremal activity, which may differ strongly from free energy minima. We discuss connections of these results to random first-order transition theory of glasses, which motivates an extension of the analysis to random-field Ising models where the dynamical activity is not symmetric under magnetisation reversal.

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Dong, Mengxia. "Existence of Extremal Functions for Higher-Order Caffarelli–Kohn–Nirenberg Inequalities." Advanced Nonlinear Studies 18, no. 3 (August 1, 2018): 543–53. http://dx.doi.org/10.1515/ans-2017-6037.

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Abstract Though there has been an extensive study on first-order Caffarelli–Kohn–Nirenberg inequalities, not much is known for the existence of extremal functions for higher-order ones. The higher-order derivative of the Caffarelli–Kohn–Nirenberg inequality established by Lin [14] states \bigg{(}\int_{\mathbb{R}^{N}}\lvert D^{j}u|^{r}\frac{dx}{|x|^{s}}\bigg{)}^{% \frac{1}{r}}\leq C\bigg{(}\int_{\mathbb{R}^{N}}\lvert D^{m}u|^{p}\frac{dx}{|x|% ^{\mu}}\bigg{)}^{\frac{a}{p}}\bigg{(}\int_{\mathbb{R}^{N}}\lvert u|^{q}\frac{% dx}{|x|^{\sigma}}\bigg{)}^{\frac{1-a}{q}}, where {C=C(p,q,r,\mu,\sigma,s,m,j)} and {p,q,r,\mu,\sigma,s,m,j} are parameters satisfying some balanced conditions. The main purpose of this paper is to establish the existence of extremal functions for a family of this higher-order derivatives of Caffarelli–Kohn–Nirenberg inequalities under numerous circumstances of parameters. Moreover, we study the compactness of the weighted Sobolev space for higher-order derivatives and prove that {\dot{H}^{m,p}_{\mu}(\Omega)\cap L^{q}_{\sigma}(\Omega)\hookrightarrow\dot{H}^% {j,r}_{s}(\Omega)} is a compact embedding within some range of the parameters.

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Kvasnica, Jozef. "Oscillations of concentrations in multicomponent diffusion." Collection of Czechoslovak Chemical Communications 54, no. 4 (1989): 892–99. http://dx.doi.org/10.1135/cccc19890892.

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While selfdiffusion coefficients Dii are always positive, the stability conditions admit both signs of the interdiffusion coefficients Dij (i ≠ j). In a multicomponent system (n > 2) with opposite signs of interdiffusion (at least within some range of concentrations and temperatures) there might occur anomalous evolution of concentrations, e.g. the damped oscillations of extremal values for some x2/t.

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Okay, Cihan, Michael Zurel, and Robert Raussendorf. "On the extremal points of the Lambda polytopes and classical simulation of quantum computation with magic states." Quantum Information and Computation 21, no. 13&14 (September 2021): 1091–110. http://dx.doi.org/10.26421/qic21.13-14-2.

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We investigate the $\Lambda$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $\Lambda_n$, for every number $n$ of qubits. We establish two properties of the family $\{\Lambda_n, n\in \mathbb{N}\}$, namely (i) Any extremal point (vertex) $A_\alpha \in \Lambda_m$ can be used to construct vertices in $\Lambda_n$, for all $n>m$. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to the classical simulation based on the preimage $A_\alpha$. In addition, we describe a new class of vertices in $\Lambda_2$ which is outside the known classification. While the hardness of classical simulation remains an open problem for most extremal points of $\Lambda_n$, the above results extend efficient classical simulation of quantum computations beyond the presently known range.

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Phalitnonkiat, Pakawat, Peter G. M. Hess, Mircea D. Grigoriu, Gennady Samorodnitsky, Wenxiu Sun, Ellie Beaudry, Simone Tilmes, et al. "Extremal dependence between temperature and ozone over the continental US." Atmospheric Chemistry and Physics 18, no. 16 (August 21, 2018): 11927–48. http://dx.doi.org/10.5194/acp-18-11927-2018.

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Abstract. The co-occurrence of heat waves and pollution events and the resulting high mortality rates emphasize the importance of the co-occurrence of pollution and temperature extremes. Through the use of extreme value theory and other statistical methods, tropospheric surface ozone and temperature extremes and their joint occurrence are analyzed over the United States during the summer months (JJA) using measurements and simulations of the present and future climate and chemistry. Five simulations from the Chemistry-Climate Model Initiative (CCMI) reference experiment using specified dynamics (REFC1SD) were analyzed: the CESM1 CAM4-chem, CHASER, CMAM, MOCAGE and MRI-ESM1r1 simulations. In addition, a 25-year present-day simulation branched off the CCMI REFC2 simulation in the year 2000 and a 25-year future simulation branched off the CCMI REFC2 simulation in 2100 were analyzed using CESM1 CAM4-chem. The last two simulations differed in their concentration of carbon dioxide (representative of the years 2000 and 2100) but were otherwise identical. In general, regions with relatively high ozone extremes over the US do not occur in regions of relatively high temperature extremes. A new metric, the spectral density, is developed to measure the joint extremal dependence of ozone and temperature by evaluating the spectral dependence of their extremes. While in many areas of the country ozone and temperature are highly correlated overall, the correlation is significantly reduced when examined on the higher end of the distributions. Measures of spectral density are less than about 0.35 everywhere, suggesting that at most only about a third of the time do extreme temperatures coincide with extreme ozone. Two regions of the US have the strongest measured extreme dependence of ozone and temperature: the northeast and the southeast. The simulated future increase in temperature and ozone is primarily due to a shift in their distributions, not to an increase in their extremes. The locations where the right-hand side of the temperature distribution does increase (by up to 30 %) are consistent with locations where soil–moisture feedback may be expected. Future changes in the right-hand side of the ozone distribution range regionally between +20 % and −10 %. The location of future increases in the high-end tail of the ozone distribution are weakly related to those of temperature with a correlation of 0.3. However, the regions where the temperature extremes increase are not located where the extremes in ozone are large, suggesting a muted ozone response.

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Crabb, M. J., and C. M. McGregor. "Interpolation and inequalities for functions of exponential type: the Arens irregularity of an extremal algebra." Glasgow Mathematical Journal 35, no. 3 (September 1993): 325–26. http://dx.doi.org/10.1017/s0017089500009897.

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For any compact convex set K ⊂ ℂ there is a unital Banach algebra Ea(K) generated by an element h in which every polynomial in h attains its maximum norm over all Banach algebras subject to the numerical range V(h) being contained in K, [1]. In the case of K a line segment in ℝ, we show here that Ea(K) does not have Arens regular multiplication. We also show that ideas about Ea(K) give simple proofs of, and extend, two inequalities of C. Frappier [4].

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Martinez-Moreno, J., and A. Rodriguez-Palacios. "Imbedding elements whose numerical range has a vertex at zero in holomorphic semigroups." Proceedings of the Edinburgh Mathematical Society 28, no. 1 (February 1985): 91–95. http://dx.doi.org/10.1017/s0013091500003229.

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If a is an element of a complex unital Banach algebra whose numerical range is confined to a closed angular region with vertex at zero and angle strictly less than π, we imbed a in a holomorphic semigroup with parameter in the open right half plane.There has been recently a great development in the theory of semigroups in Banach algebras (see [6]), with attention focused on the relation between the structure of a given Banach algebra and the existence of continuous or holomorphic non-trivial semigroups with certain properties with range in this algebra. The interest of this paper arises from the fact that we relate in it, we think for the first time, this new point of view in the theory of Banach algebras with the already classic one of numerical ranges [2,3]. The proofs of our results use, in addition to some basic ideas from numerical ranges in Banach algebras, the concept of extremal algebra Ea(K) of a compact convex set K in ℂ due to Bollobas [1] and concretely the realization of Ea(K) achieved by Crabb, Duncan and McGregor [4].

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Stegeman, Alwin. "Extremal behavior of heavy-tailed ON-periods in a superposition of ON/OFF processes." Advances in Applied Probability 34, no. 1 (March 2002): 179–204. http://dx.doi.org/10.1239/aap/1019160956.

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Empirical studies of data traffic in high-speed networks suggest that network traffic exhibits self-similarity and long-range dependence. Cumulative network traffic has been modeled using the so-called ON/OFF model. It was shown that cumulative network traffic can be approximated by either fractional Brownian motion or stable Lévy motion, depending on how many sources are active in the model. In this paper we consider exceedances of a high threshold by the sequence of lengths of ON-periods. If the cumulative network traffic converges to stable Lévy motion, the number of exceedances converges to a Poisson limit. The same holds in the fractional Brownian motion case, provided a very high threshold is used. Finally, we show that the number of exceedances obeys the central limit theorem.

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Stegeman, Alwin. "Extremal behavior of heavy-tailed ON-periods in a superposition of ON/OFF processes." Advances in Applied Probability 34, no. 01 (March 2002): 179–204. http://dx.doi.org/10.1017/s0001867800011459.

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Empirical studies of data traffic in high-speed networks suggest that network traffic exhibits self-similarity and long-range dependence. Cumulative network traffic has been modeled using the so-called ON/OFF model. It was shown that cumulative network traffic can be approximated by either fractional Brownian motion or stable Lévy motion, depending on how many sources are active in the model. In this paper we consider exceedances of a high threshold by the sequence of lengths of ON-periods. If the cumulative network traffic converges to stable Lévy motion, the number of exceedances converges to a Poisson limit. The same holds in the fractional Brownian motion case, provided a very high threshold is used. Finally, we show that the number of exceedances obeys the central limit theorem.

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Chernitskii, Alexander A. "Fundamental interactions and quantum behavior in unified field theory." International Journal of Modern Physics A 35, no. 02n03 (January 30, 2020): 2040021. http://dx.doi.org/10.1142/s0217751x20400217.

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The concept of unified field theory is discussed. Two nonlinear field models with world volume type action are considered, namely extremal space-time film model and Born–Infeld nonlinear electrodynamics. The natural appearance of two long-range fundamental interactions, electromagnetism and gravitation, in these field models is discussed. The quantum behavior of the interacting solitons-particles is considered. The concept of quasi-bounding quantization in nonlinear field models is introduced.

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Golbabai, Ahmad, Nima Safaei, and Mahboubeh Molavi-Arabshahi. "Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method." Entropy 24, no. 10 (September 23, 2022): 1345. http://dx.doi.org/10.3390/e24101345.

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This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

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Basu, Pallab. "Energy scales in a holographic black hole and conductivity at finite momentum." Canadian Journal of Physics 89, no. 3 (March 2011): 271–76. http://dx.doi.org/10.1139/p11-019.

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In this work we discuss the low temperature (T) behavior of gauge field correlators with finite momentum (k) in a AdS4 black hole background. At low temperature, a substantial nonzero conductivity is only possible for a frequency range ω > ωg = k. This tallies with the simple fact that at least an amount of energy ωg is needed to create an excitation of momentum k. Due to the existence of this “gap”, one may expect that at the zero frequency limit the real part of momentum-dependent conductivity falls exponentially with 1/T. Using analytic methods, we found a exp(–ωc/T) falloff of the real part of conductivity with inverse temperature. Interestingly, ωg ≠ ωc. From the above results, we speculate that the “degrees of freedom”, say carriers, different than quasiparticle excitation determines conductivity at the low temperature and the low-frequency limit. Here ωc < ωg, and we may calculate their ratios analytically. We also discuss similar issues at a finite chemical potential. The situation is rather different for an extremal blackhole. A zero temperature extremal blackhole does not show a sharp gap for the finite momentum excitations, and the real part of the conductivity is always nonzero for any nonzero frequency ω. However, the real part of the conductivity goes to zero at the ω → 0 limit. Not surprisingly, we find a power-law decay with temperature for the same quantity, as the extremal limit is approached.

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Pereira, L., and H. Ferreira. "Limiting crossing probabilities of random fields." Journal of Applied Probability 43, no. 3 (September 2006): 884–91. http://dx.doi.org/10.1239/jap/1158784955.

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Random fields on , with long-range weak dependence for each coordinate individually, usually present clustering of high values. For each one of the eight directions in , we formulate restriction conditions on local occurrence of two or more crossings of high levels. These smooth oscillation conditions enable computation of the extremal index as a clustering measure from the limiting mean number of crossings. In fact, only four directions must be inspected since for opposite directions we find the same local path crossing behaviour and the same limiting mean number of crossings. The general theory is illustrated with several 1-dependent nonstationary random fields.

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Pereira, L., and H. Ferreira. "Limiting crossing probabilities of random fields." Journal of Applied Probability 43, no. 03 (September 2006): 884–91. http://dx.doi.org/10.1017/s0021900200002199.

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Random fields on , with long-range weak dependence for each coordinate individually, usually present clustering of high values. For each one of the eight directions in , we formulate restriction conditions on local occurrence of two or more crossings of high levels. These smooth oscillation conditions enable computation of the extremal index as a clustering measure from the limiting mean number of crossings. In fact, only four directions must be inspected since for opposite directions we find the same local path crossing behaviour and the same limiting mean number of crossings. The general theory is illustrated with several 1-dependent nonstationary random fields.

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Meijin Luo, Yusong Lu. "The Primitive Exponent Set of a Class of Representative Twocolored Digraph in Graph Theory." Journal of Electrical Systems 20, no. 2 (April 4, 2024): 271–81. http://dx.doi.org/10.52783/jes.1173.

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Graph is simple and intuitive. It can be used to solve many problems in computer science. For a kind of representativedigraph, the edges (arcs) of the digraph are colored with red and blue colors. The range of the primitive exponent are discussed indifferent cases, and the extremal two-colored digraphs are found by coloring all arcs with two colors. Finally, the primitive exponentset is given. The results can provide a reference for the study of primitive exponent of three-colored digraph and the application ofgraph coloring in computer science, such as communication network and coding cache.

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Chernitskii, Alexander A. "Induced gravitation in nonlinear field models." International Journal of Modern Physics: Conference Series 41 (January 2016): 1660119. http://dx.doi.org/10.1142/s2010194516601198.

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The description of gravitation in the framework of soliton interaction is considered for two nonlinear field models. These models are Born — Infeld nonlinear electrodynamics and so-called Born — Infeld type scalar field model. The last model can also be called the extremal space-time film one because of the specific form of the appropriate variational principle. Gravitational interaction is considered in the context of unification for all interactions of material particles. It is shown that long-range interaction of solitons of the models appears as force one and metrical one. The force interaction can be interpreted as electromagnetic one. The metrical interaction can be interpreted as gravitational one.

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Sánchez-Sánchez, M., M. A. Sordo, A. Suárez-Llorens, and E. Gómez-Déniz. "DERIVING ROBUST BAYESIAN PREMIUMS UNDER BANDS OF PRIOR DISTRIBUTIONS WITH APPLICATIONS." ASTIN Bulletin 49, no. 1 (November 23, 2018): 147–68. http://dx.doi.org/10.1017/asb.2018.36.

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AbstractWe study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models.

Journal articles on the topic 'Extremal range'

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