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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.

In this paper, closed ideals in Cc(X), the functionally countable subalgebra of C(X), with the mc-topology, is studied. We show that if X 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 and F is an ec-filter on X, then F is an ec-ultrafilter if and only if it is a zc-ultrafilter.

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)}.

Let $f_1, f_2, \ldots, f_n$ be fixed nonzero real-valued functions on $\mathbb{R}$, the real numbers. Let $\varphi_n(X_n)= \big(x_1^2f_1^2+x_2^2f_2^2+ \ldots + x_n^2f_n^2 \big)^{\frac{1}{2}}$, where $X_n=(x_1, x_2, \ldots, x_n) \in \mathbb{R}^n$. We show that $\varphi_n$ has properties similar to a norm on the normed linear space. Although $\varphi_n$ is not a norm on $\mathbb{R}^n$ in general, it induces a norm on $\mathbb{R}^n$. For the nonzero function $F : \mathbb{R}^2 \to \mathbb{R}$, a curvature formula for the implicit curve $G(x, y)=F^2(x, y)=0$ at any regular point is given. A similar result is presented when $F$ is a nonzero function from $\mathbb{R}^3$ to $\mathbb{R}$. In continued, we concentrate on $F(x, y)=\int_a^b \varphi_2(x, y)dt$. It is shown that the curvature of $F(x, y)=c$ when $c>0$ is a positive multiple of $c^2$. Particularly, we observe that $F(x, y)=\int_0^{\frac{\pi}{2}} \sqrt{x^2 \cos^2 t + y^2 \sin^2 t} dt$ is an elliptic integral of the second kind.

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).

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).

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.