Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Inguinal plasty and appendectomy as treatment for Amyand's hernia: case report and literature review

Amyand's hernia is described as the presence of the caecal appendix within the hernial sac of an incarcerated inguinal hernia. It was reported as an incidental finding in 1% of cases and with evidence of appendicitis in 0.1% of cases. The approach involves performing appendectomy and inguinal repair in the same surgical time, depending on the clinical scenario and the surgeon's decisions. We presented the case of a 76-year-old male patient with a diagnosis of Amyand's right inguinal hernia diagnosed during trans-operative right inguinal plasty

Duals of variable exponent Hörmander spaces (0<p−≤p+≤10< p^- \le p^+ \le 1) and some applications

In this paper we characterize the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' of the variable exponent H\"or\-man\-der space \B^c_{p(\cdot)} (\Omega) when the exponent $p(\cdot)$ satisfies the conditions $0 < p^- \le p^+ \le 1$, the Hardy-Littlewood maximal operator $M$ is bounded on $L_{p(\cdot)/p_0}$ for some $0 < p_0 < p^-$ and $\Omega$ is an open set in $\R^n$. It is shown that the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' is isomorphic to the H\"ormander space \B^{\mathrm{loc}}_\infty (\Omega) (this is the $p^+ \le 1$ counterpart of the isomorphism \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' \simeq \B^{\mathrm{loc}}_{\widetilde{p'(\cdot)}} (\Omega), $1 < p^- \le p^+ < \infty$, recently proved by the authors) and hence the representation theorem \bigl( \B^c_{p(\cdot)} (\Omega) \bigr)' \simeq l^{\N}_\infty is obtained. Our proof relies heavily on the properties of the Banach envelopes of the steps of \B^c_{p(\cdot)} (\Omega) and on the extrapolation theorems in the variable Lebesgue spaces of entire analytic functions obtained in a precedent paper. Other results for $p(\cdot) \equiv p$, $0 < p < 1$, are also given (e.g. \B^c_p (\Omega) does not contain any infinite-dimensional $q$-Banach subspace with $p < q \le 1$ or the quasi-Banach space \B_p \cap \E'(Q) contains a copy of $l_p$ when $Q$ is a cube in $\R^n$). Finally, a question on complex interpolation (in the sense of Kalton) of variable exponent H\"ormander spaces is proposed.J. Motos is partially supported by grant MTM2011-23164 from the Spanish Ministry of Science and Innovation. The authors wish to thank the referees for the careful reading of the manuscript and for many helpful suggestions and remarks that improved the exposition. In particular, the remark immediately following Theorem 2.1 and the Question 2 were motivated by the comments of one of them.Motos Izquierdo, J.; Planells Gilabert, MJ.; Talavera Usano, CF. (2015). Duals of variable exponent Hörmander spaces ($0< p^- \le p^+ \le 1$) and some applications. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 109(2):657-668. https://doi.org/10.1007/s13398-014-0209-zS6576681092Aboulaich, R., Meskine, D., Souissi, A.: New diffussion models in image processing. Comput. Math. Appl. 56(4), 874–882 (2008)Acerbi, E., Mingione, G.: Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164(3), 213–259 (2002)Bastero, J.: $$l^q$$ l q -subspaces of stable $$p$$ p -Banach spaces, $$0 < p \le 1$$ 0 < p ≤ 1 . Arch. Math. (Basel) 40, 538–544 (1983)Boas, R.P.: Entire functions. Academic Press, London (1954)Boza, S.: Espacios de Hardy discretos y acotación de operadores. Dissertation, Universitat de Barcelona (1998)Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue spaces, foundations and harmonic analysis. Birkhäuser, Basel (2013)Cruz-Uribe, D.: SFO, A. Fiorenza, J. M. Martell, C. Pérez: The boundedness of classical operators on variable $$L^p$$ L p spaces. Ann. Acad. Sci. Fenn. Math. 31, 239–264 (2006)Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and sobolev spaces with variable exponents. lecture notes in mathematics, vol. 2007. Springer, Berlin, Heidelberg (2011)Hörmander, L.: The analysis of linear partial operators II, Grundlehren 257. Springer, Berlin, Heidelberg (1983)Hörmander, L.: The analysis of linear partial operators I, Grundlehren 256. Springer, Berlin, Heidelberg (1983)Kalton, N.J., Peck, N.T., Roberts, J.W.: An $$F$$ F -space sampler, London Mathematical Society Lecture Notes, vol. 89. Cambridge University Press, Cambridge (1985)Kalton, N.J.: Banach envelopes of non-locally convex spaces. Canad. J. Math. 38(1), 65–86 (1986)Kalton, N.J., Mitrea, M.: Stability results on interpolation scales of quasi-Banach spaces and applications. Trans. Am. Math. Soc. 350(10), 3903–3922 (1998)Kalton, N.J.: Quasi-Banach spaces, Handbook of the Geometry of Banach Spaces, vol. 2. In: Johnson, W.B., Lindenstrauss, J. (eds.), pp. 1099–1130. Elsevier, Amsterdam (2003)Köthe, G.: Topological vector spaces I. Springer, Berlin, Heidelberg (1969)Motos, J., Planells, M.J., Talavera, C.F.: On variable exponent Lebesgue spaces of entire analytic functions. J. Math. Anal. Appl. 388, 775–787 (2012)Motos, J., Planells, M.J., Talavera, C.F.: A note on variable exponent Hörmander spaces. Mediterr. J. Math. 10, 1419–1434 (2013)Stiles, W.J.: Some properties of $$l_p$$ l p , $$0 < p < 1$$ 0 < p < 1 . Studia Math. 42, 109–119 (1972)Triebel, H.: Theory of function spaces. Birkhäuser, Basel (1983)Vogt, D.: Sequence space representations of spaces of test functions and distributions. In: Zapata, G.I. (ed.) Functional analysis, holomorphy and approximation theory, Lecture Notes in Pure and Applied Mathematics, vol. 83, pp. 405–443 (1983

Quantifying Robotic Swarm Coverage

In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation. This work fills that gap by introducing an error metric that provides a quantitative measure of coverage for use with any control scheme. The proposed error metric is continuously sensitive to changes in the swarm distribution, unlike commonly used discretization methods. We analyze the theoretical and computational properties of the error metric and propose two benchmarks to which error metric values can be compared. The first uses the realizable extrema of the error metric to compute the relative error of an observed swarm distribution. We also show that the error metric extrema can be used to help choose the swarm size and effective radius of each robot required to achieve a desired level of coverage. The second benchmark compares the observed distribution of error metric values to the probability density function of the error metric when robot positions are randomly sampled from the target distribution. We demonstrate the utility of this benchmark in assessing the performance of stochastic control algorithms. We prove that the error metric obeys a central limit theorem, develop a streamlined method for performing computations, and place the standard statistical tests used here on a firm theoretical footing. We provide rigorous theoretical development, computational methodologies, numerical examples, and MATLAB code for both benchmarks.Comment: To appear in Springer series Lecture Notes in Electrical Engineering (LNEE). This book contribution is an extension of our ICINCO 2018 conference paper arXiv:1806.02488. 27 pages, 8 figures, 2 table

Neuromuscular and acute symptoms responses to progressive elastic resistance exercise in patients with chronic obstructive pulmonary disease:Cross-sectional study

BACKGROUND: Quadriceps muscle training is a key part in the rehabilitation of chronic obstructive pulmonary disease (COPD) patients. However, exercise intensity prescription and progression with the typically used elastic bands is challenging. We aimed to evaluate neuromuscular, acute symptoms and cardiorespiratory responses (heart rate and dyspnea) during progressive elastic resistance exercise in patients with COPD. METHODS: Fourteen patients diagnosed with moderate-very severe COPD performed knee extensions at different elastic resistance levels (i.e., colors). The neuromuscular activity was recorded using surface electromyography for the rectus femoris, vastus lateralis and vastus medialis, together with rate of perceived exertion, perceived quadriceps fatigue, dyspnea, oxygen saturation and heart rate. RESULTS: For the vastus lateralis and rectus femoris, increase of muscle activity was evident from a two-level increment when using the red color. For the vastus medialis, there were no muscle activity progressions. Dyspnea, quadriceps fatigue and especially rate of perceived exertion increased in a dose-response fashion and were correlated with the resistance level and muscle activity at the three muscles. CONCLUSION: Heavy elastic resistance exercise is feasible in COPD patients without excessive dyspnea and a stable cardiorespiratory response. In general, at least two elastic resistance increments are needed to enhance muscle activity for the vastus lateralis and rectus femoris, while there is no increase for the vastus medialis. These results may help to individualize exercise dosing during elastic resistance training in patients with COPD

Maximal operator in variable exponent generalized morrey spaces on quasi-metric measure space

We consider generalized Morrey spaces on quasi-metric measure spaces , in general unbounded, with variable exponent p(x) and a general function defining the Morrey-type norm. No linear structure of the underlying space X is assumed. The admission of unbounded X generates problems known in variable exponent analysis. We prove the boundedness results for maximal operator known earlier only for the case of bounded sets X. The conditions for the boundedness are given in terms of the so called supremal inequalities imposed on the function , which are weaker than Zygmund-type integral inequalities often used for characterization of admissible functions . Our conditions do not suppose any assumption on monotonicity of in r

The Stokes and Poisson problem in variable exponent spaces

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur

Characterization of relapsing-remitting multiple sclerosis patients using support vector machine classifications of functional and diffusion MRI data.

Multiple Sclerosis patients' clinical symptoms do not correlate strongly with structural assessment done with traditional magnetic resonance images. However, its diagnosis and evaluation of the disease's progression are based on a combination of this imaging analysis complemented with clinical examination. Therefore, other biomarkers are necessary to better understand the disease. In this paper, we capitalize on machine learning techniques to classify relapsing-remitting multiple sclerosis patients and healthy volunteers based on machine learning techniques, and to identify relevant brain areas and connectivity measures for characterizing patients. To this end, we acquired magnetic resonance imaging data from relapsing-remitting multiple sclerosis patients and healthy subjects. Fractional anisotropy maps, structural and functional connectivity were extracted from the scans. Each of them were used as separate input features to construct support vector machine classifiers. A fourth input feature was created by combining structural and functional connectivity. Patients were divided in two groups according to their degree of disability and, together with the control group, three group pairs were formed for comparison. Twelve separate classifiers were built from the combination of these four input features and three group pairs. The classifiers were able to distinguish between patients and healthy subjects, reaching accuracy levels as high as 89% ± 2%. In contrast, the performance was noticeably lower when comparing the two groups of patients with different levels of disability, reaching levels below 63% ± 5%. The brain regions that contributed the most to the classification were the right occipital, left frontal orbital, medial frontal cortices and lingual gyrus. The developed classifiers based on MRI data were able to distinguish multiple sclerosis patients and healthy subjects reliably. Moreover, the resulting classification models identified brain regions, and functional and structural connections relevant for better understanding of the disease

Percepción de autoeficacia vs. rechazo del uso del condón en las prácticas sexuales de mujeres y hombres jóvenes/Self-efficacy perception vs. rejection of condom use in the sexual practices of young women and men.

En las relaciones sexuales de jóvenes, las variables asociadas al uso del condón son diversas y comúnmente se presentan con otras variables que, a su vez, se asocian con la práctica sexual desprotegida. Los objetivos de este estudio consistieron en determinar en qué medida la percepción de auto eficacia, la baja percepción de riesgo y el rechazo del uso del condón se relacionan con el uso del condón en las relaciones sexuales de jóvenes colombianos. Participaron en él 308 estudiantes universitarios de la ciudad de Cúcuta, Colombia. Los resultados indican correlaciones significativas en hombres entre el uso del condón y la percepción de auto eficacia, y correlaciones negativas en mujeres entre el uso del condón, la baja percepción de riesgo y el rechazo del uso del condón. Solo en el grupo de hombres, la percepción de autoeficacia predice el uso del condón