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Journal articles on the topic 'Decomposition for BV functions'

Author: Grafiati

Published: 14 March 2023

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1

Bianchini, Stefano, and Daniela Tonon. "A decomposition theorem for $BV$ functions." Communications on Pure and Applied Analysis 10, no. 6 (May 2011): 1549–66. http://dx.doi.org/10.3934/cpaa.2011.10.1549.

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2

Song, Yingqing, Xiaoping Yang, and Zhenghai Liu. "DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHÉODORY SPACES." Acta Mathematica Scientia 23, no. 4 (October 2003): 433–39. http://dx.doi.org/10.1016/s0252-9602(17)30485-x.

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3

del Álamo, Miguel, and Axel Munk. "Total variation multiscale estimators for linear inverse problems." Information and Inference: A Journal of the IMA 9, no. 4 (March 2, 2020): 961–86. http://dx.doi.org/10.1093/imaiai/iaaa001.

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Abstract Even though the statistical theory of linear inverse problems is a well-studied topic, certain relevant cases remain open. Among these is the estimation of functions of bounded variation ($BV$), meaning $L^1$ functions on a $d$-dimensional domain whose weak first derivatives are finite Radon measures. The estimation of $BV$ functions is relevant in many applications, since it involves minimal smoothness assumptions and gives simplified, interpretable cartoonized reconstructions. In this paper, we propose a novel technique for estimating $BV$ functions in an inverse problem setting and provide theoretical guaranties by showing that the proposed estimator is minimax optimal up to logarithms with respect to the $L^q$-risk, for any $q\in [1,\infty )$. This is to the best of our knowledge the first convergence result for $BV$ functions in inverse problems in dimension $d\geq 2$, and it extends the results of Donoho (1995, Appl. Comput. Harmon. Anal., 2, 101–126) in $d=1$. Furthermore, our analysis unravels a novel regime for large $q$ in which the minimax rate is slower than $n^{-1/(d+2\beta +2)}$, where $\beta$ is the degree of ill-posedness: our analysis shows that this slower rate arises from the low smoothness of $BV$ functions. The proposed estimator combines variational regularization techniques with the wavelet-vaguelette decomposition of operators.

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4

Parasidis, I. N., and E. Providas. "Factorization method for solving nonlocal boundary value problems in Banach space." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 103, no. 3 (September 30, 2021): 76–86. http://dx.doi.org/10.31489/2021m3/76-86.

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This article deals with the factorization and solution of nonlocal boundary value problems in a Banach space of the abstract form B1u = Au − SΦ(u) − GΨ(A0u) = f, u ∈ D(B1),where A, A0 are linear abstract operators, S, G are vectors of functions, Φ, Ψ are vectors of linear bounded functionals, and u, f are functions. It is shown that the operator B1 under certain conditions can be factorized into a product of two simpler lower order operators as B1 = BB0. Then the solvability and the unique solution of the equation B1u = f easily follow from the solvability conditions and the unique solutions of the equations Bv = f and B0u = v. The universal technique proposed here is essentially different from other factorization methods in the respect that it involves decomposition of both the equation and boundary conditions and delivers the solution in closed form. The method is implemented to solve ordinary and partial Fredholm integro-differential equations.

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5

Tang, Liming, and Chuanjiang He. "Multiscale Image Representation and Texture Extraction Using Hierarchical Variational Decomposition." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/107120.

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In order to achieve a mutiscale representation and texture extraction for textured image, a hierarchical(BV,Gp,L2)decomposition model is proposed in this paper. We firstly introduce the proposed model which is obtained by replacing the fixed scale parameter of the original(BV,Gp,L2)decomposition with a varying sequence. And then, the existence and convergence of the hierarchical decomposition are proved. Furthermore, we show the nontrivial property of this hierarchical decomposition. Finally, we introduce a simple numerical method for the hierarchical decomposition, which utilizes gradient decent for energy minimization and finite difference for the associated gradient flow equations. Numerical results show that the proposed hierarchical(BV,Gp,L2)decomposition is very appropriate for multiscale representation and texture extraction of textured image.

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6

Anzellotti, G., S. Delladio, and G. Scianna. "BV Functions over rectifiable currents." Annali di Matematica Pura ed Applicata 170, no. 1 (December 1996): 257–96. http://dx.doi.org/10.1007/bf01758991.

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7

Williams, Stephen A., and Richard C. Scalzo. "Differential games and BV functions." Journal of Differential Equations 59, no. 3 (September 1985): 296–313. http://dx.doi.org/10.1016/0022-0396(85)90143-3.

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8

sci, global. "Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups." Analysis in Theory and Applications 37, no. 3 (June 2021): 311–29. http://dx.doi.org/10.4208/ata.2021.lu80.03.

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9

Araujo, Jesuś. "Linear isometries between spaces of functions of bounded variation." Bulletin of the Australian Mathematical Society 59, no. 2 (April 1999): 335–41. http://dx.doi.org/10.1017/s0004972700032949.

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Given two subsets X and Y of ℝ each with at least two points, we describe the surjective linear isometries between the spaces of functions of bounded variation BV(X) and BV(Y): namely, if T : BV(X) → BV(Y) is such an isometry, then there exist α ∈ ℂ, |α| = 1, and a monotonic bijective map h : Y → X such that (Tf)(y) = αf(h(y)) for every f ∈ BV(X) and every y ∈ Y.

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10

Cheng, Yong, Yahan Yang, Zao Jiang, Longjun Xu, and Chenglun Liu. "Fabrication and Characterization of a Novel Composite Magnetic Photocatalyst β-Bi2O3/BiVO4/MnxZn1−xFe2O4 for Rhodamine B Degradation under Visible Light." Nanomaterials 10, no. 4 (April 21, 2020): 797. http://dx.doi.org/10.3390/nano10040797.

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β-Bi2O3/BiVO4/MnxZn1−xFe2O4 (BV/MZF) composite magnetic photocatalyst was first synthesized using the hydrothermal and calcination method. BV/MZF was a mesoporous material with most probable pore size and specific surface area of 18 nm and 17.84 m2/g, respectively. Due to its high saturation magnetization (2.67 emu/g), the BV/MZF composite can be easily separated and recovered from solution under an external magnetic field. The results of photo-decomposition experiments show that the decomposition rate of Rhodamine B (RhB) by BV/MZF can reach 92.6% in 3 h under visible light. After three cycles, BV/MZF can still maintain structural stability and excellent pollutant degradation effect. In addition, analysis of the photocatalytic mechanism of BV/MZF for RhB shows that the p-n heterojunction formed in BV/MZF plays a vital role in its photocatalytic performance. This work has potential application in the future for solving environmental pollution.

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11

LA TORRE, DAVIDE, FRANKLIN MENDIVIL, and EDWARD R. VRSCAY. "ITERATED FUNCTION SYSTEMS ON FUNCTIONS OF BOUNDED VARIATION." Fractals 24, no. 02 (June 2016): 1650019. http://dx.doi.org/10.1142/s0218348x16500195.

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We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.

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12

Bellettini, Giovanni, Maurizio Paolini, Franco Pasquarelli, and Giuseppe Scianna. "Covers, soap films and BV functions." Geometric Flows 3, no. 1 (March 1, 2018): 57–75. http://dx.doi.org/10.1515/geofl-2018-0005.

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Abstract In this paper we review the double covers method with constrained BV functions for solving the classical Plateau’s problem. Next, we carefully analyze some interesting examples of soap films compatible with covers of degree larger than two: in particular, the case of a soap film only partially wetting a space curve, a soap film spanning a cubical frame but having a large tunnel, a soap film that retracts to its boundary, and various soap films spanning an octahedral frame.

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13

Greco, Luigi, and Roberta Schiattarella. "An embedding theorem for BV-functions." Communications in Contemporary Mathematics 22, no. 04 (May 24, 2019): 1950032. http://dx.doi.org/10.1142/s0219199719500329.

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14

Ambrosio, Luigi, Michele Miranda, Stefania Maniglia, and Diego Pallara. "BV functions in abstract Wiener spaces." Journal of Functional Analysis 258, no. 3 (February 2010): 785–813. http://dx.doi.org/10.1016/j.jfa.2009.09.008.

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15

Astudillo-Villalba, Franklin R., and Julio C. Ramos-Fernández. "Multiplication operators on the space of functions of bounded variation." Demonstratio Mathematica 50, no. 1 (April 25, 2017): 105–15. http://dx.doi.org/10.1515/dema-2017-0012.

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Abstract In this paper,we study the properties of the multiplication operator acting on the bounded variation space BV[0, 1]. In particular,we show the existence of non-null compact multiplication operators on BV[0, 1] and non-invertible Fredholm multiplication operators on BV[0, 1].

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16

Hu, Yawen, Rebecca A. Hill, and Masami Yoshimura. "Role of Adenylyl Cyclase Type 7 in Functions of BV-2 Microglia." International Journal of Molecular Sciences 24, no. 1 (December 25, 2022): 347. http://dx.doi.org/10.3390/ijms24010347.

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To assess the role of adenylyl cyclase type 7 (AC7) in microglia’s immune function, we generated AC7 gene knockout (AC7 KO) clones from a mouse microglial cell line, BV-2, using the CRISPR-Cas9 gene editing system. The ability of BV-2 cells to generate cAMP and their innate immune functions were examined in the presence or absence of ethanol. The parental BV-2 cells showed robust cAMP production when stimulated with prostaglandin-E1 (PGE1) and ethanol increased cAMP production in a dose-dependent manner. AC7 KO clones of BV-2 cells showed diminished and ethanol-insensitive cAMP production. The phagocytic activity of the parental BV-2 cells was inhibited in the presence of PGE1; AC7 KO BV-2 cells showed lower and PGE1-insensitive phagocytic activity. Innate immune activities of the parental BV-2 cells, including bacterial killing, nitric oxide synthesis, and expression of arginase 1 and interleukin 10 were activated as expected with small effects of ethanol. However, the innate immune activities of AC7 KO cells were either drastically diminished or not detected. The data presented suggest that AC7 has an important role in the innate immune functions of microglial cells. AC7’s involvement in ethanol’s effects on immune functions remains unclear. Further studies are needed.

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17

Fleischer and Porter. "CONVERGENCE OF METRIC SPACE-VALUED BV FUNCTIONS." Real Analysis Exchange 27, no. 1 (2001): 315. http://dx.doi.org/10.2307/44154127.

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18

Amar, Micol, and Virginia De Cicco. "A new approximation result for BV-functions." Comptes Rendus Mathematique 340, no. 10 (May 2005): 735–38. http://dx.doi.org/10.1016/j.crma.2005.03.027.

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19

Nguyen, Hoai-Minh. "$\Gamma$ -convergence, Sobolev norms, and BV functions." Duke Mathematical Journal 157, no. 3 (April 2011): 495–533. http://dx.doi.org/10.1215/00127094-1272921.

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20

Fathi, Javad, and Alireza Ahmadi Ledari. "Relations between BV*(q;α) and Λ*BVp classes of functions." Georgian Mathematical Journal 25, no. 3 (September 1, 2018): 349–55. http://dx.doi.org/10.1515/gmj-2017-0066.

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AbstractThe aim of this paper is to establish the relation between the two classes of functions {\mathrm{BV}_{*}(q;\alpha)} and {\Lambda_{*}\mathrm{BV}^{p}}. It uses a new shorter proof and extends the results of Gogatishvili, Goginava and Tephnadze.

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21

Conti, Sergio, Matteo Focardi, and Flaviana Iurlano. "Which special functions of bounded deformation have bounded variation?" Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 1 (October 17, 2017): 33–50. http://dx.doi.org/10.1017/s030821051700004x.

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Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV), but are less well understood. We discuss here the relation to BV under additional regularity assumptions, which may require the regular part of the strain to have higher integrability or the jump set to have finite area or the Cantor part to vanish. On the positive side, we prove that BD functions that are piecewise affine on a Caccioppoli partition are in GSBV, and we prove that SBDp functions are approximately continuous -almost everywhere away from the jump set. On the negative side, we construct a function that is BD but not in BV and has distributional strain consisting only of a jump part, and one that has a distributional strain consisting of only a Cantor part.

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22

Darji. "DECOMPOSITION OF FUNCTIONS." Real Analysis Exchange 21, no. 1 (1995): 19. http://dx.doi.org/10.2307/44153859.

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23

LIU, FENG. "A REMARK ON THE REGULARITY OF THE DISCRETE MAXIMAL OPERATOR." Bulletin of the Australian Mathematical Society 95, no. 1 (December 1, 2016): 108–20. http://dx.doi.org/10.1017/s0004972716000940.

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We study the regularity properties of several classes of discrete maximal operators acting on $\text{BV}(\mathbb{Z})$ functions or $\ell ^{1}(\mathbb{Z})$ functions. We establish sharp bounds and continuity for the derivative of these discrete maximal functions, in both the centred and uncentred versions. As an immediate consequence, we obtain sharp bounds and continuity for the discrete fractional maximal operators from $\ell ^{1}(\mathbb{Z})$ to $\text{BV}(\mathbb{Z})$.

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24

Monteiro, Giselle A. "On Kurzweil-Stieltjes equiintegrability and generalized BV functions." Mathematica Bohemica 144, no. 4 (August 19, 2019): 423–36. http://dx.doi.org/10.21136/mb.2019.0041-19.

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25

Pugach, P., and V. Shlyk. "Moduli, capacity, BV-functions on the Riemann surfaces." Lobachevskii Journal of Mathematics 38, no. 2 (March 2017): 338–51. http://dx.doi.org/10.1134/s1995080217020172.

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26

Dávila, Juan, and Radu Ignat. "Lifting of BV functions with values in S1." Comptes Rendus Mathematique 337, no. 3 (August 2003): 159–64. http://dx.doi.org/10.1016/s1631-073x(03)00314-5.

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27

Kreuml, Andreas, and Olaf Mordhorst. "Fractional Sobolev norms and BV functions on manifolds." Nonlinear Analysis 187 (October 2019): 450–66. http://dx.doi.org/10.1016/j.na.2019.06.014.

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28

Conze, Jean-Pierre, and Stéphane Le Borgne. "On the CLT for rotations and BV functions." Comptes Rendus Mathematique 357, no. 2 (February 2019): 212–15. http://dx.doi.org/10.1016/j.crma.2019.01.008.

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29

Lunardi, Alessandra, Michele Miranda, and Diego Pallara. "BV Functions on Convex Domains in Wiener Spaces." Potential Analysis 43, no. 1 (January 29, 2015): 23–48. http://dx.doi.org/10.1007/s11118-015-9462-9.

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30

Ambrosio, Luigi, and Valentino Magnani. "Weak differentiability of BV functions on stratified groups." Mathematische Zeitschrift 245, no. 1 (September 1, 2003): 123–53. http://dx.doi.org/10.1007/s00209-003-0530-2.

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31

Nguyen, Hoai-Minh, and Marco Squassina. "On anisotropic Sobolev spaces." Communications in Contemporary Mathematics 21, no. 01 (January 28, 2019): 1850017. http://dx.doi.org/10.1142/s0219199718500177.

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We investigate two types of characterizations for anisotropic Sobolev and BV spaces. In particular, we establish anisotropic versions of the Bourgain–Brezis–Mironescu formula, including the magnetic case both for Sobolev and BV functions.

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32

Martio, Olli. "Functions of bounded variation and curves in metric measure spaces." Advances in Calculus of Variations 9, no. 4 (October 1, 2016): 305–22. http://dx.doi.org/10.1515/acv-2014-0045.

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AbstractAn approximation modulus, the $\mathrm{AM}$-modulus, for a family of paths is introduced in a metric measure space ${(X,d,\nu)}$. It is shown that a function of bounded variation in X is a BV function on almost every path with respect to the $\mathrm{AM}$-modulus. Properties of the $\mathrm{AM}$-modulus, its relations to the usual ${M_{1}}$-modulus and to the BV-capacities of condensers are studied. Only minimal assumptions on X and the measure ν are employed.

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33

Athavale, Prashant, and Eitan Tadmor. "Integro-Differential Equations Based on $(BV, L^1)$ Image Decomposition." SIAM Journal on Imaging Sciences 4, no. 1 (January 2011): 300–312. http://dx.doi.org/10.1137/100795504.

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34

Yu, Dansheng, and Songping Zhou. "On relations among Fourier coefficients and sum-functions." Studia Scientiarum Mathematicarum Hungarica 45, no. 3 (September 1, 2008): 301–19. http://dx.doi.org/10.1556/sscmath.2008.1052.

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35

Meng, Xiangling, Yu Liu, and Xiangyun Xie. "Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation." Fractal and Fractional 5, no. 4 (December 18, 2021): 280. http://dx.doi.org/10.3390/fractalfract5040280.

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In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theorem. We also establish the Dunkl BV capacity and investigate some measure theoretic properties, moreover, we show that the Dunkl BV capacity and the Hausdorff measure of codimension one have the same null sets. Finally, we develop the characterization of a heat semigroup of the Dunkl-bounded variation space, thereby giving its relation to the functions of Dunkl-bounded variation.

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36

Beeldman, Emma, Joost Raaphorst, Michelle Klein Twennaar, Rosanne Govaarts, Yolande A. L. Pijnenburg, Rob J. de Haan, Marianne de Visser, and Ben A. Schmand. "The cognitive profile of behavioural variant FTD and its similarities with ALS: a systematic review and meta-analysis." Journal of Neurology, Neurosurgery & Psychiatry 89, no. 9 (February 9, 2018): 995–1002. http://dx.doi.org/10.1136/jnnp-2017-317459.

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Approximately 30% of patients with amyotrophic lateral sclerosis (ALS) have cognitive impairment and 8%–14% fulfil the criteria for behavioural variant frontotemporal dementia (bv-FTD). The cognitive profiles of ALS and bv-FTD have been reported to be comparable, but this has never been systematically investigated. We aimed to determine the cognitive profile of bv-FTD and examine its similarities with that of ALS, to provide evidence for the existence of a cognitive disease continuum encompassing bv-FTD and ALS. We therefore systematically reviewed neuropsychological studies on bv-FTD patients and healthy volunteers. Neuropsychological tests were divided in 10 cognitive domains and effect sizes were calculated for all domains and compared with the cognitive profile of ALS by means of a visual comparison and a Pearson’s r correlation coefficient. We included 120 studies, totalling 2425 bv-FTD patients and 2798 healthy controls. All cognitive domains showed substantial effect sizes, indicating cognitive impairment in bv-FTD patients compared to healthy controls. The cognitive domains with the largest effect sizes were social cognition, verbal memory and fluency (1.77–1.53). The cognitive profiles of bv-FTD and ALS (10 cognitive domains, 1287 patients) showed similarities on visual comparison and a moderate correlation 0.58 (p=0.13). When social cognition, verbal memory, fluency, executive functions, language and visuoperception were considered, i.e. the cognitive profile of ALS, Pearson’s r was 0.73 (p=0.09), which raised to 0.92 (p=0.03), when language was excluded in this systematic analysis of patients with a non-language subtype of FTD. The cognitive profile of bv-FTD consists of deficits in social cognition, verbal memory, fluency and executive functions and shows similarities with the cognitive profile of ALS. These findings support a cognitive continuum encompassing ALS and bv-FTD.

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37

Lee, Myung Gyoon. "HII regions and young star clusters in the Magellanic Clouds." Symposium - International Astronomical Union 148 (1991): 207–8. http://dx.doi.org/10.1017/s0074180900200387.

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Using U BV CCD photometry, the stellar content of HII regions and young star clusters in the Magellanic Clouds has been studied: (1) the reddenings have been determined, and ages of OB associations and young star clusters have been measured; (2) the stellar initial mass functions have been determined by using the main-sequence luminosity functions; and (3) U BV CCD surface photometry of nine young star clusters has been obtained and their structural properties investigated.

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38

Liu, Feng, and Lei Xu. "Regularity of one-sided multilinear fractional maximal functions." Open Mathematics 16, no. 1 (December 31, 2018): 1556–72. http://dx.doi.org/10.1515/math-2018-0129.

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AbstractIn this paper we introduce and investigate the regularity properties of one-sided multilinear fractional maximal operators, both in continuous case and in discrete case. In the continuous setting, we prove that the one-sided multilinear fractional maximal operators$\mathfrak{M}_\beta^{+}\; \text{and}\, \mathfrak{M}_\beta^{-}$map W1,p1 (ℝ)×· · ·×W1,pm (ℝ) into W1,q(ℝ) with 1 < p1, … , pm < ∞, 1 ≤ q < ∞ and $1/q= \sum_{i=1}^m1/p_i-\beta$, boundedly and continuously. In the discrete setting, we show that the discrete one-sided multilinear fractional maximal operators are bounded and continuous from ℓ1(ℤ)×· · ·×ℓ1(ℤ) to BV(ℤ). Here BV(ℤ) denotes the set of functions of bounded variation defined on ℤ. Our main results represent significant and natural extensions of what was known previously.

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39

Buffa, Vito, and Michele Miranda Jr. "Rough traces of BV functions in metric measure spaces." Annales Fennici Mathematici 46, no. 1 (June 2021): 309–33. http://dx.doi.org/10.5186/aasfm.2021.4625.

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40

Don, Sebastiano, and Davide Vittone. "A compactness result for BV functions in metric spaces." Annales Academiae Scientiarum Fennicae Mathematica 44, no. 1 (February 2019): 329–39. http://dx.doi.org/10.5186/aasfm.2019.4415.

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41

Casas, Eduardo, Florian Kruse, and Karl Kunisch. "Optimal Control of Semilinear Parabolic Equations by BV-Functions." SIAM Journal on Control and Optimization 55, no. 3 (January 2017): 1752–88. http://dx.doi.org/10.1137/16m1056511.

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42

Pinamonti, Andrea, Marco Squassina, and Eugenio Vecchi. "Magnetic BV-functions and the Bourgain–Brezis–Mironescu formula." Advances in Calculus of Variations 12, no. 3 (July 1, 2019): 225–52. http://dx.doi.org/10.1515/acv-2017-0019.

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AbstractWe prove a general magnetic Bourgain–Brezis–Mironescu formula which extends the one obtained in [37] in the Hilbert case setting. In particular, after developing a rather complete theory of magnetic bounded variation functions, we prove the validity of the formula in this class.

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43

Buczolich, Zoltan, Thierry De Pauw, and Washek F. Pfeffer. "Charges, BV Functions, and Multipliers for Generalized Riemann Integrals." Indiana University Mathematics Journal 48, no. 4 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1818.

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44

Burago, Yu D., and N. N. Kosovskiĭ. "The trace of $BV$-functions on an irregular subset." St. Petersburg Mathematical Journal 22, no. 2 (April 1, 2011): 251. http://dx.doi.org/10.1090/s1061-0022-2010-01139-7.

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45

BĚLÍK, PAVEL, and MITCHELL LUSKIN. "APPROXIMATION BY PIECEWISE CONSTANT FUNCTIONS IN A BV METRIC." Mathematical Models and Methods in Applied Sciences 13, no. 03 (March 2003): 373–93. http://dx.doi.org/10.1142/s0218202503002556.

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We study the approximation properties of piecewise constant functions with respect to triangular and rectangular finite elements in a metric defined on functions of bounded variation. We apply our results to a thin film model for martensitic crystals and to the approximation of deformations with microstructure.

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46

Ponce, Augusto C., and Daniel Spector. "On formulae decoupling the total variation of BV functions." Nonlinear Analysis: Theory, Methods & Applications 154 (May 2017): 241–57. http://dx.doi.org/10.1016/j.na.2016.08.028.

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47

Lahti, Panu. "Approximation of BV by SBV functions in metric spaces." Journal of Functional Analysis 279, no. 11 (December 2020): 108763. http://dx.doi.org/10.1016/j.jfa.2020.108763.

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48

Park, Soojin, Jinju Kim, Minkyu Shin, Moochang Hong, and Hyunsu Bae. "The effect of bee venom on ovalbumin-induced asthma model (55.13)." Journal of Immunology 186, no. 1_Supplement (April 1, 2011): 55.13. http://dx.doi.org/10.4049/jimmunol.186.supp.55.13.

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Abstract Asthma is a chronic disease marked by airway hyperreactivity and inflammation. Bee venom(BV) has been traditionally used in oriental medicine to relieve pain and to treat chronic inflammatory diseases. Some recent reports suggest that BV maybe an effective treatment for patients with asthma. However, there are still some unanswered questions relating to efficacy of BV therapy in asthma. The CD4+CD25+Foxp3+ regulatory T cell(Treg) play an important role in regulating the immune response. Treg can reduce inflammation and allergic reactions through its inhibitory functions. In this study, we reasoned that BV inhibits inflammatory diseases by effect on Treg and examined the effect of BV in naïve mice. Diverse concentration was treated everyday for 5days and BV significantly expanded Treg on 1mg/kg concentration. This result proposes that BV can attenuate asthma. We used 7-10 weeks female Balb/c mice were sensitized with ovalbumin(OVA). As a result, BV decreased inflammatory cytokine secretion including IL-4, IL-5, IL-13 in bronchoalveolar lavage(BAL) fluid. Also BV was significantly decrease structural remodeling of the airway. The number of Neutrophil, Lymphocyte, Macrophage, and total cells were significantly lower in the BV group than the OVA group. These results suggest that BV has potential therapeutic value for controlling asthma responses resulting from exposure to allergens.

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Borwein, J. M., and A. S. Lewis. "Decomposition of Multivariate Functions." Canadian Journal of Mathematics 44, no. 3 (June 1, 1992): 463–82. http://dx.doi.org/10.4153/cjm-1992-030-9.

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AbstractGiven a bivariate function defined on some subset of the Cartesian product of two sets, it is natural to ask when that function can be decomposed as the sum of two univariate functions. In particular, is a pointwise limit of such functions itself decomposable? At first glance this might seem obviously true but, as we show, the possibilities are quite subtle. We consider the question of existence and uniqueness of such decompositions for this case and for many generalizations to multivariate functions and to cases where the sets and functions have topological or measure theoretic structure.

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50

Kozen, Dexter, Susan Landau, and Richard Zippel. "Decomposition of Algebraic Functions." Journal of Symbolic Computation 22, no. 3 (March 1996): 235–46. http://dx.doi.org/10.1006/jsco.1996.0051.

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