Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials

Belovas, Igoris

doi:10.3390/math10060865

Cited by 2 publications

(3 citation statements)

References 17 publications

(23 reference statements)

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“…For example, random measurement errors, temperature or rainfall in a certain area all obey a normal distribution. According to the central limit theorem [ 31 ], if a given random variable is dominated by a large number of tiny, independent random factors, the individual effects of each factor are relatively uniform and no one factor has a clear advantage, andthe random variable approximately obeys a normal distribution. The normal distribution is the limiting distribution of many important probability distributions [ 32 ].…”

Section: Methodsmentioning

confidence: 99%

Causal Analysis and Prevention Measures for Extreme Heavy Rainstorms in Zhengzhou to Protect Human Health

Liu

2022

Behavioral Sciences

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This study focused on the extreme heavy rainstorm that occurred in Zhengzhou in July 2021; approximately 380 people were killed or missing as a result of this storm. To investigate the evolution behaviors of this rainstorm and take corresponding prevention measures, several methods and models were adopted, including cloud modeling, preliminary hazard analysis (PHA), fault tree analysis (FTA), bow-tie modeling, and chaos theory. The main reasons for this rainstorm can be divided into the following three aspects: force majeure, such as terrain and extreme weather conditions, issues with city construction, and insufficient emergency rescue. The secondary disasters caused by this rainstorm mainly include urban water logging, river flooding, and mountain torrents and landslides. The main causes of the subway line-5 accident that occurred can be described as follows: the location of the stabling yard was low, the relevant rules and regulations of the subway were not ideal, insufficient attention was given to the early warning information, and the emergency response mechanism was not ideal. Rainstorms result from the cross-coupling of faults in humans, objects, the environment, and management subsystems, and the evolution process shows an obvious butterfly effect. To prevent disasters caused by rainstorms, the following suggestions should be adopted: vigorously improve the risk awareness and emergency response capabilities of leading cadres, improve the overall level of urban disaster prevention and mitigation, reinforce the existing reservoirs in the city, strengthen the construction of sponge cities, and improve the capacity of urban disaster emergency rescue.

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Section: Methodsmentioning

confidence: 99%

Causal Analysis and Prevention Measures for Extreme Heavy Rainstorms in Zhengzhou to Protect Human Health

Liu

2022

Behavioral Sciences

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“…Pusiau eksponentinė generuojanti funkcija duoda mums pirmos eilės charakteristinę diferencialinę lygtį (žr. 1 lentelę C priede [2] ir 3 teoremą [3]), tuo metu kai paprastoji ir eksponentinė generuojančios funkcijos tenkina antros eilės dalinių išvestinių charakteristinę diferencialinę lygtį.…”

Section: Generuojančiu ˛Funkciju ˛Metodasunclassified

“…2.3 Uždaviniai studentams 1 uždavinys. Tegu ψ 1,2 , ψ 2,1 , ψ 2,2 ̸ = 0 ir skaičiai a n,k yra generuoti matricos 3 .…”

Section: Generuojančiu ˛Funkciju ˛Metodasunclassified

Problems for combinatorial numbers satisfying a class of triangular arrays

Belovas

2023

LMR

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Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first and the second types, non-central Stirling numbers, Eulerian numbers, Lah numbers, and their generalizations. In this work, we derive the general analytic expression of the numbers satisfying a class of triangular arrays and propose problems (both teaching and unsolved ones) for undergraduates studying probability theory and analytical combinatorics subjects in the study programs of the fields of mathematics and computer science. Some of the unsolved challenges can also be used as the basis for a thesis.

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Central Limit Theorems for Combinatorial Numbers Associated with Laguerre Polynomials

Cited by 2 publications

References 17 publications

Causal Analysis and Prevention Measures for Extreme Heavy Rainstorms in Zhengzhou to Protect Human Health

Causal Analysis and Prevention Measures for Extreme Heavy Rainstorms in Zhengzhou to Protect Human Health

Problems for combinatorial numbers satisfying a class of triangular arrays

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