• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.117-125
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• 2020

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.17 no.32
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• pp.7-16
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• 1994

In the existing deterministic network, the capacity of each arc has determined property. But actually, it may be a property which cannot be determined. Even though it should be determining, it contains many errors. In treating these kinds of problems, fuzzy theory is suitable. Recently, due to development the study on complicated and indefinited systems which contain fuzziness could be possible. This paper includes that the capacity of each arc and the goal quantity with nonnegative integer have the fuzziness. The object is to search the new mathod of fuzzy maximal flow quantity. If the degree of arc membership function of the minimal cut part is not larger than that of arc membership function of the part except the minimal cut, first calcurate nonfuzzy maximal flow quantity, and then can compute the optimal quantity the 3rd step at one time with Max-Min fuzzy operating in the arc capacity of minimal cut and the goal quantity without a great number of recalculation.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1057-1072
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• 2023

Let 𝜑 : ℝⁿ × [0, ∞) → [0, ∞) be a growth function and H^𝜑(ℝⁿ) the Musielak-Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called 𝜃-summability is considered for multi-dimensional Fourier transforms in H^𝜑(ℝⁿ). Precisely, with some assumptions on 𝜃, the authors first prove that the maximal operator of the 𝜃-means is bounded from H^𝜑(ℝⁿ) to L^𝜑(ℝⁿ). As consequences, some norm and almost everywhere convergence results of the 𝜃-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner-Riesz, Weierstrass and Picard-Bessel summations, are also presented.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.615-623
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• 1995

Consider a function m defined in $R^n$ and the associated convolution operator T given by the Fourier transform $\hat{T} = m\hat{f}$.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1233-1241
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• 2007

We derive a kind of weighted norm inequalities which relate the commutators of potential type operators to the corresponding maximal operators.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.65-72
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• 1998

We investigate a chain of properties of real function algebras along the analogous proofs of the complex cases such as the fact that any real function algebra which is both maximal and essential is pervasive. And some properties of real function algebras with a vertex property will be discussed.

• Physical Therapy Rehabilitation Science
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• v.7 no.4
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• pp.147-153
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• 2018

Objective: This study investigated the effects of air stacking training (AST) on pulmonary function, respiratory strength, and peak cough flow (PCF) in persons with cervical spinal cord injury (CSCI). Design: Randomized controlled trial. Methods: A total of 24 persons with CSCI were randomly allocated to the AST group (n=12) or the incentive spirometry training (IST) group (n=12). Patients with CSCI received AST or IST for 15 minutes, with 3 sessions per week for 4 weeks, and all groups performed basic exercises for 15 minutes. In the AST group, after the subject inhaled the maximal amount of air as best as possible, the therapist insufflated additional air into the patient's lung using an oral nasal mask about 2-3 times. In the IST group, patients were allowed to hold for three seconds at the maximum inspiration and then to breathe. The pre and post-tests measured forced vital capacity (FVC), forced expiratory volume one at second (FEV1), maximal expiratory pressure (MEP), maximal inspiratory pressure (MIP) and PCF. Results: Both groups showed significant improvements in FVC, FEV1, MEP, MIP and PCF values after training (p<0.05). The FVC in the post-test and the mean change of FVC, FEV1, MIP were significantly higher in the AST group than the IST group (p<0.05). Conclusions: The findings of this study suggested that AST significantly improved pulmonary function, respiratory strength, and PCF in persons with CSCI. Therefore, AST should be included in respiratory rehabilitation programs to improve coughing ability, pulmonary function and respiratory muscle strength.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.