• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.41-47
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• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.375-391
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• 1994

In 1968k Cameron and Storvick introduced the analytic and the sequential operator-valued function space integral [2]. Since then, the theo교 of the analytic operator-valued function space integral has been investigated by many mathematicians - Cameron, Storvick, Johnson, Skoug, Lapidus, Chang and author etc. But there are not that many papers related to the theory of the sequential operator-valued function space integral. In this paper, we establish the existence of the sequential operator-valued function space integral as an operator from $L_p$ to $L_p'(1 and investigated the integral equation related to this integral.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.165-171
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• 2008

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1234-1239
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• 2017

Basic research on the accelerator-driven system is conducted by combining $^{235}U$-fueled and $^{232}Th$-loaded cores in the Kyoto University Critical Assembly with the pulsed neutron generator (14 MeV neutrons) and the proton beam accelerator (100 MeV protons with a heavy metal target). The results of experimental subcriticality are presented with a wide range of subcriticality level between near critical and 10,000 pcm, as obtained by the pulsed neutron source method, the Feynman-${\alpha}$ method, and the neutron source multiplication method.

• Nuclear Engineering and Technology
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• v.53 no.7
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• pp.2133-2150
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• 2021

In this work, Esfahan light water subcritical reactor (ELWSCR) is analysed using experimental and theoretical diagnostic methods. Important neutronic parameters of the system such as prompt neutron lifetime, delayed neutron fraction, prompt neutron decay constant, negative reactivity of the core, fuel and moderator temperature coefficient of reactivity, and overall and local void coefficient of reactivity are estimated. Also, neutron flux distribution, reflector saving, water level effect, and lattice pitch of the core including operating point of the facility are studied in details. Theoretical results are calculated by MCNPX and measurements are performed utilizing zero power reactor noise method. Detailed descriptions of the results are explained in the text.

• Electronics and Telecommunications Trends
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• v.36 no.6
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• pp.67-77
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• 2021

Since Richard Feynman presented the concept of quantum computers, quantum computing have been identified today overcoming the limits of supercomputing in various applications. Quantum hardware has steadily developed into 50 to hundreds of qubits of various quantum hardware technologies based on superconductors, semiconductors, and trapped ions over 40 years. However, it is possible to use a NISQ (Noisy Intermediate Scale Quantum) level quantum device that currently has hardware constraints. In addition, the software environment in which quantum algorithms for problem solving in various applications can be executed is pursuing research with quantum computing software such as programming language, compiler, control, testing and verification. The development of quantum software is essential amid intensifying technological competition for the commercialization of quantum computers. Therefore, this paper introduces the trends of the latest technology, focusing on quantum computing software platforms, and examines important software component technologies.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.451-470
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• 2020

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition 0 = t₀ < t₁ < ⋯ < t_n < t_n+1 = T of [0, T], define X_n : C[0, T] → ℝⁿ⁺¹ by X_n(x) = (x(t₀), x(t₁), …, x(t_n)). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X_n which has a drift and does not contain the present position of paths. As applications of the formula with X_n, we evaluate the Radon-Nikodym derivatives of the functions ∫₀^T[x(t)]^mdλ(t)(m∈ℕ) and [∫₀^Tx(t)dλ(t)]² on C[0, T], where λ is a complex-valued Borel measure on [0, T]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C[0, T].

• Journal of The Korean Association For Science Education
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• v.32 no.8
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• pp.1295-1317
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• 2012

There has been disagreement on the importance of definitions in science education. Yager (1983) believes that one crisis in science education was due to the considerable emphasis upon the learning of definitions. Hobson (2004) disagrees with physics textbooks that do not provide general definition on energy. Some textbooks explain that "there is no completely satisfactory definition of energy" or they can only "struggle to define it." In general, imprecise definitions in textbooks (Bauman, 1992) and inaccuracies in definition provided by teachers (Galili & Lehavi, 2006) may cause alternative conceptions. Besides, there are at least four challenges in defining physical concepts: precision, circularity, context and completeness in knowledge. These definitional problems that have been discussed in The Feynman Lectures, may impede the learning of physical concepts. A meta-study approach is employed to examine about five hundreds journal papers that may discuss definitions in physics, problems in defining physical concepts and how they may result in alternative conceptions. These journal papers are mainly selected from journals such as American Journal of Physics, International Journal of Science Education, Journal of Research in Science Teaching, Physics Education, The Physics Teachers, and so on. There are also comparisons of definitions with definitions from textbooks, Dictionaries of Physics, and English Dictionaries. To understand the nature of alternative conception, Lee et al. (2010) have suggested a theoretical framework to describe the learning issues by synthesizing cognitive psychology and science education approaches. Taking it a step further, this study incorporates the challenges in semantics and epistemology, proposes that there are at least four variants of alternative conceptions. We may coin the term, 'alternative definitions', to refer to the commonly available definitions, which have these four problems in defining physics concepts. Based on this study, alternative definitions may result in at least four variants of alternative conceptions. Note that these four definitional problems or challenges in definitions cannot be easily resolved. Educators should be cognizant of the four variants of alternative conceptions which can arise from alternative definitions. The concepts of alternative definitions can be useful and possibly generalized to science education and beyond.

• Nuclear Engineering and Technology
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• v.55 no.7
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• pp.2447-2453
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• 2023

The radioactivity concentrations of Naturally Occurring Radioactive Materials (NORM) i.e., ²²⁶Ra, ²³²Th, and ⁴K in various chemical fertilizers being used in the agricultural soil of Pakistan were determined utilizing gamma spectrometry by employing a High Purity Germanium (HPGe) detector. The radioactivity concentrations of ²²⁶Ra, ²³²Th, and ⁴K extended from 2.58 ± 0.8-265.7 ± 8.8 Bq kg^-1, 1.53 ± 0.14-76.6 ± 1.07 Bq kg^-1 and 36.5 ± 1.34-15606.7 ± 30.2 Bq kg^-1 respectively. The radiological hazard parameters such as internal and external indices and annual effective dose rates were calculated, while excessive lifetime cancer risk factors for the indoor and outdoor areas were found in the range from 0.3×10^-3 to 10.723×10^-3 and 0.03×10^-3 to 2.7948×10^-3 of most fertilizers, however, some values were slightly higher than the UNSCEAR (The United Nations Scientific Committee on the Effects of Atomic Radiation) recommended values for potash-containing fertilizers such as MOP (Muriate of Potash).