Closed ideals in the functionally countable subalgebra of C(X)

[EN] In this paper, closed ideals in Cc(X), the functionally countable subalgebra of C(X), with the mc-topology, is studied. We show that ifX is CUC-space, then C*c(X) with the uniform norm-topology is a Banach algebra. Closed ideals in Cc(X) as a modified countable analogue of closed ideals in C(X) with the m-topology are characterized. For a zero-dimensional space X, we show that a proper ideal in Cc(X) is closed if and only if it is an intersection of maximal ideals of Cc(X). It is also shown that every ideal in Cc(X) with the mc-topology is closed if and only if X is a P-space if and only if every ideal in C(X) with the m-topology is closed. Moreover, for a strongly zero-dimensional space X, it is proved that a properly closed ideal in C*c(X) is an intersection of maximal ideals of C*c(X) if and only if X is pseudo compact. Finally, we show that if X is a P-space, then the family of ec-ultrafilters and zc-ultrafilter coincide.  Veisi, A. (2022). Closed ideals in the functionally countable subalgebra of C(X). Applied General Topology. 23(1):79-90. https://doi.org/10.4995/agt.2022.15844OJS799023

Metric spaces related to Abelian groups

[EN] When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology. In this paper, we are studying G-metric spaces based on L-groups (i.e., partially ordered groups which are lattices). Some results in G-metric spaces are obtained. The G-metric topology is defined which is further studied for its topological properties. We prove that if G is a densely ordered group or an infinite cyclic group, then every G-metric space is Hausdorff. It is shown that if G is a Dedekind-complete densely ordered group, (X, d) a G-metric space, A ⊆ X and d is bounded, then f : X → G with f(x) = d(x, A) := inf{d(x, a) : a ∈ A} is continuous and further x ∈ clXA if and only if f(x) = e (the identity element in G). Moreover, we show that if G is a densely ordered group and further a closed subset of R, K(X) is the family of nonempty compact subsets of X, e < g ∈ G and d is bounded, then d′ (A, B) < g if and only if A ⊆ Nd(B, g) and B ⊆ Nd(A, g), where Nd(A, g) = {x ∈ X : d(x, A) < g}, dB(A) = sup{d(a, B) : a ∈ A} and d′ (A, B) = sup{dA(B), dB(A)}.The authors are grateful to the referee for providing helpful comments and recommendations to improve the quality of the paper.Veisi, A.; Delbaznasab, A. (2021). Metric spaces related to Abelian groups. Applied General Topology. 22(1):169-181. https://doi.org/10.4995/agt.2021.14446OJS169181221A. Arhangel'skii and M. Tkachenko, Topological groups and related structures, Atlantis press/ World Scientific, Amsterdam-Paris, 2008. https://doi.org/10.2991/978-94-91216-35-0R. Engelking, General topology, Sigma Ser. Pure Math., Vol. 6, Heldermann Verlag, Berlin, 1989.L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, Berlin/Heidelberg/New York, 1976.I. Kaplansky, Infinite Abelian Groups, University of Michigan Press, 1954.O. A. S. Karamzadeh, M. Namdari and S. Soltanpour, On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol. 16, no. 2 (2015), 183-207. https://doi.org/10.4995/agt.2015.3445M. Namdari and A. Veisi, Rings of quotients of the subalgebra of C(X) consisting of functions with countable image, Inter. Math. Forum 7 (2012), 561-571.D. J. S. Robinson, A course in the theory of groups, second edition, Springer-Verlag New York, Inc. 1996.J. Rotman, An Introduction to the Theory of Groups, Vol. 148, 4th edition Springer, New York, 1995.A. Veisi, The subalgebras of the functionally countable subalgebra of C(X), Far East J. Math. Sci. (FJMS) 101, no. 10 (2017), 2285-2297. https://doi.org/10.17654/MS101102285A. Veisi, Invariant norms on the subalgebras of $C(X)$ consisting of bounded functions with countable image, JP Journal of Geometry and Topology 21, no. 3 (2018), 167-179. https://doi.org/10.17654/GT021030167A. Veisi, ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X), Appl. Gen. Topol. 20, no. 2 (2019), 395-405. https://doi.org/10.4995/agt.2019.11524A. Veisi and A. Delbaznasab, New structure of norms on Rn and their relations with the curvature of the plane curves, Ratio Mathematica 39 (2020), 55-67.S. Willard, General Topology, Addison-Wesley, 1970

ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)

[EN] The purpose of this article is to study and investigate ec-filters on X and ec-ideals in C*c (X) in which they are in fact the counterparts of zc-filters on X and zc-ideals in Cc(X) respectively. We show that the maximal ideals of C*c (X) are in one-to-one correspondence with the ec-ultrafilters on X. In addition, the sets of ec-ultrafilters and zc-ultrafilters are in one-to-one correspondence. It is also shown that the sets of maximal ideals of Cc(X) and C*c (X) have the same cardinality. As another application of the new concepts, we characterized maximal ideals of C*c (X). Finally, we show that whether the space X is compact, a proper ideal I of Cc(X) is an ec-ideal if and only if it is a closed ideal in Cc(X) if and only if it is an intersection of maximal ideals of Cc(X).Veisi, A. (2019). ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X). Applied General Topology. 20(2):395-405. https://doi.org/10.4995/agt.2019.11524SWORD395405202F. Azarpanah, Intersection of essential ideals in C(X), Proc. Amer. Math. Soc. 125 (1997), 2149-2154. https://doi.org/10.1090/S0002-9939-97-04086-0R. Engelking, General Topology, Heldermann Verlag Berlin, 1989.A. A. Estaji, A. Karimi Feizabadi and M. Abedi, Zero-sets in point-free topology and strongly z-ideals, Bull. Iranian Math. Soc. 41, no. 5 (2015), 1071-1084.N. J. Fine, L. Gillman and J. Lambek, Rings of quotients of rings of functions, Lecture Notes Series Mc-Gill University Press, Montreal, 1966.M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, On functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova 129 (2013), 47-69. https://doi.org/10.4171/RSMUP/129-4L. Gillman and M. Jerison, Rings of continuous functions, Springer-Verlag, 1976.M. Henriksen, R. Raphael and R. G. Woods, $SP$-scattered spaces; a new generalization of scattered spaces, Comment. Math. Univ. Carolin. 48, no. 3 (2007), 487-505.O. A. S. Karamzadeh, M. Namdari and S. Soltanpour, On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol. 16, no. 2 (2015), 183-207. https://doi.org/10.4995/agt.2015.3445O. A. S. Karamzadeh and M. Rostami, On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93 (1985), 179-184. https://doi.org/10.2307/2044578M. R. Koushesh, The Banach algebra of continuous bounded functions with separable support, Studia Mathematica 210, no. 3 (2012), 227-237. https://doi.org/10.4064/sm210-3-3R. Levy and M. D. Rice, Normal P-spaces and the $G_delta$-topology, Colloq. Math. 47 (1981), 227-240. https://doi.org/10.4064/cm-44-2-227-240M. A. Mulero, Algebraic properties of rings of continuous functions, Fund. Math. 149 (1996), 55-66.M. Namdari and A. Veisi, Rings of quotients of the subalgebra of C(X) consisting of functions with countable image, Inter. Math. Forum 7 (2012), 561-571.D. Rudd, On two sum theorems for ideals of C(X), Michigan Math. J. 17 (1970), 139-141. https://doi.org/10.1307/mmj/1029000423W. Rudin, Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8 (1957), 39-42. https://doi.org/10.1090/S0002-9939-1957-0085475-7A. Veisi, The subalgebras of the functionally countable subalgebra of C(X), Far East J. Math. Sci. (FJMS) 101, no. 10 (2017), 2285-2297. https://doi.org/10.17654/MS101102285A. Veisi, Invariant norms on the functionally countable subalgebra of C(X) consisting of bounded functions with countable image, JP Journal of Geometry and Topology 21, no. 3 (2018), 167-179. https://doi.org/10.17654/GT021030167S. Willard, General Topology, Addison-Wesley, 1970

Fuzzy fractional-order sliding mode control of COVID-19 virus variants

These days, one of the biggest challenges in the world is dealing with the outbreak of the Covid 19 virus. Recently, new variants of this virus have been identified that have a much higher rate of transmission. To effectively control and manage the spread of the disease, a clear understanding of its transmission dynamics and effective control techniques to reduce or inhibit the spread of the virus is necessary. Although vaccine production and distribution are currently underway, Non-Pharmacological Interventions (NPI) continue to be an important and fundamental strategy for controlling the spread of the virus in various countries around the world. In this paper, Covid 19 dynamics is modeled using four well-known categories (SEIR): Susceptible-Exposed-Infected-Recovered. Since the parameters of the model have uncertainty, a robust control method should be designed. In this paper, using fractional calculus and fuzzy logic, a robust fuzzy fractional-order sliding mode controller (FOFSMC) for Covid 19 dynamics is proposed, which aims to control the prevalence of the disease using NPI. The proposed method is implemented both on the integer and fractional order model. Finally, the performance of the proposed controller on the new variant of the Covid 19 virus with a faster disease transmission rate will be evaluated

Effects of microencapsulated Lactobacillus rhamnosus JCM 1136 probiotics on blood parameters and body composition of rainbow trout

Effects of the microencapsulated Lactobacillus rhamnosus JCM 1136 on the blood parameters and body composition of rainbow trout (Oncorhynchus mykiss). In this study, first the probiotic bacteria L. rhamnosus JCM1136 were microencapsulated with coatings of sodium alginate and chitosan. Then, they were added to the food pellets and given to the fingerlings. For this purpose, 225 rainbow trout fingerlings (6.23 ± 0.17 g) in 5 treatments and each treatment with 3 replications were placed in California trays (220 × 30 × 15 cm). Treatment 1 (T1): Fish fed with 108 CFU/g microencapsulated probiotics with sodium alginate, treatment 2 (T2): fish fed with 108 CFU/g microencapsulated probiotics with sodium alginate and chitosan, treatment 3 (T3): fish fed with 108 CFU/g capsule-free probiotics, treatment 4 (T4): fish fed with probiotic-free sodium alginate-chitosan capsules and control treatment 5 (T5): fish fed with commercial free-probiotic and capsules pellets. At the end of the course, results indicated that the fishes fed with diet containing sodium alginate-chitosan microencapsulated probiotics in terms of blood parameters such as red blood cells, white blood cells, hemoglobin and hematocrit as well as the amount of carcass protein compared to control and other treatments were in better condition, which These differences were significant with control treatments fishes (p < 0.05)

Analysis Of Solar Radiation Towards Optimization and Location Of The Urban Blocks In The Neighborhood Units

Increasing population causes Energy consumption and environmental pollution. It is essential to consider renewable forms of energy, especially solar power, to reduce energy consumption. This requires attention to energy issues in the early stages of urban design and practical and creative solutions for more efficient use of this type of energy. This study aims at calculating the annual solar radiation at a city scale through a novel process and methodology. In this regard, artificial intelligence algorithms and satellite data can help maximize the amount of sunlight in neighborhoods and urban blocks in neighborhood units during the development process. In the simulation process, location, and optimization of the urban form, it is necessary to consider the limitations and resources for field study and simulation of urban blocks. Therefore, in this study, Farhangian neighborhood in phase 1 of Kermanshah, Iran, which has a good level of structural diversity and lends itself to field studies, was selected and studied at neighborhood and urban block scales. The case study indicates the significant role of calculating and optimizing the patterns of urban blocks to achieve maximum solar energy. Estimates at different levels show that urban block variables effectively access solar radiation energy and, given various scales of development - from macro-scale spatial planning to micro-scale local design - can improve energy intake by 3 to 5 percent. Accordingly, the results show that to accelerate the calculation of energy at the planning scale, the use of 2.5D locating model and 3D optimization contribute to achieving the maximum or minimum solar radiation, respectively. On the other hand, this method can be used to organize calculations and planning for maximum absorption of solar radiation at different stages of development

Analysis Of Solar Radiation Towards Optimization and Location Of The Urban Blocks In The Neighborhood Units

Increasing population causes Energy consumption and environmental pollution. It is essential to consider renewable forms of energy, especially solar power, to reduce energy consumption. This requires attention to energy issues in the early stages of urban design and practical and creative solutions for more efficient use of this type of energy. This study aims at calculating the annual solar radiation at a city scale through a novel process and methodology. In this regard, artificial intelligence algorithms and satellite data can help maximize the amount of sunlight in neighborhoods and urban blocks in neighborhood units during the development process. In the simulation process, location, and optimization of the urban form, it is necessary to consider the limitations and resources for field study and simulation of urban blocks. Therefore, in this study, Farhangian neighborhood in phase 1 of Kermanshah, Iran, which has a good level of structural diversity and lends itself to field studies, was selected and studied at neighborhood and urban block scales. The case study indicates the significant role of calculating and optimizing the patterns of urban blocks to achieve maximum solar energy. Estimates at different levels show that urban block variables effectively access solar radiation energy and, given various scales of development - from macro-scale spatial planning to micro-scale local design - can improve energy intake by 3 to 5 percent. Accordingly, the results show that to accelerate the calculation of energy at the planning scale, the use of 2.5D locating model and 3D optimization contribute to achieving the maximum or minimum solar radiation, respectively. On the other hand, this method can be used to organize calculations and planning for maximum absorption of solar radiation at different stages of development

Mini-vitrectomy; a simple solution to a serious condition

Purpose: To evaluate the safety and efficacy of clear corneal approach irido-zonulo-hyaloido-vitrectomy, which we named “mini-vitrectomy,” in the management of pseudophakic aqueous misdirection. Methods: In this retrospective, non-comparative interventional case series, 24 eyes with diagnosis of pseudophakic aqueous misdirection were enrolled. Medical therapy with cycloplegics and laser therapy, including posterior capsulotomy and hyaloidotomy, was not effective in the management of the condition. The eyes underwent mini-vitrectomy, a simple technique in which iridotomy, zonulectomy, hyaloidectomy, and limited anterior vitrectomy were performed via a clear cornea incision. The main outcome measure was reformation of the anterior chamber, which was evaluated at day 1 and months 1, 3, 6, and 12. Results: The mean age of patients was 75.3 ± 11.3 years (range, 47 to 90), and 13 (54.2%) patients were women. Anterior chamber was deep in 22 patients (91.7%) at the last follow-up visit. The mean intraocular pressure (IOP) was 30.31 ± 1.9 mm Hg at presentation on 2.67 ± 1.09 glaucoma medications. IOP decreased significantly to 14.5 ± 4.6 mm Hg at 12-month follow-up. (P = 0.001). The number of glaucoma medications at final visit was 2.2 ± 0.9 (P = 0.21). Conclusion: Mini-vitrectomy is a simple, safe, and effective procedure in the management of pseudophakic aqueous misdirection, and it can be adopted by all ophthalmologists who are involved in glaucoma management and are not comfortable with the pars plana vitrectomy approach

Presentation of Adult-onset Asthma and Periocular Xanthogranuloma with Intermediate Uveitis and Hodgkin's Lymphoma: A Case Report

Abstract Purpose: To report a case of adult-onset asthma and periocular xanthogranuloma (AAPOX) in a patient with intermediate uveitis and a history of Hodgkin's lymphoma (HL). Case Report: A 51-year-old man with a past medical history of HL presented with blurred vision, asthma, and bilateral yellowish eyelid lesions. The eyelid lesions and asthma appeared 10 years after being diagnosed with HL. Physical examination was significant for multiple subcutaneous and firm eyelid masses in addition to the presence of pre-auricular and submandibular lymphadenopathies. Ophthalmic examination revealed bilateral intermediate uveitis and mild macular edema. Further systemic evaluations, including laboratory testing and imaging, were normal. Excisional biopsy of the eyelid lesions was performed and the histopathologic examination was consistent with the diagnosis of AAPOX. Conclusion: The presence of AAPOX in a patient with intermediate uveitis and history of HL suggests that immunological dysfunction may play a role in the pathogenesis of adult orbital xanthogranulomatous disease