A New Benzothiazin-functionalized Calix[4]arene-based Fluorescent Chemosensor for the Selective Detection of Co2+ Ion

Calixarenes, which have a great place in supramolecular chemistry, have become the most prominent macrocyclic compounds in synthetic organic chemistry due to their easy synthesis and functionalization. In this study, p-tert-butyl calix[4]arene dihydrazide derivative was synthesized and then reacted with 3-oxo-3,4-dihydro-2 H-benzo[b][1,4] thiazin-2-ylideneacetyl chloride to prepare new calixarene based chromophore compound 4. The structure of the synthesized compound was elucidated by spectroscopic methods such as ¹H NMR ¹³C NMR and FT-IR spectroscopy. Chromogenic and fluorescence properties of compound 4 were evaluated. It was observed from both studies that compound 4 was Co²⁺ selective and shows fluorescence Switched-off behavior. Stoichiometry, binding constant and the detection limit were calculated. The stoichiometry between compound 4 and Co²⁺ was found to be 1:1. The binding constant value (K) was calculated as 666.67 M^??1 using Benesi–Hildebrand equation, while the detection limit for Co²⁺ ion was calculated as 0.0465 µM.

     

Spectroscopic Studies and Crystal Structure of 4-(2-Hydroxy-3-Methoxybenzylideneamino)-<Emphasis Type="Italic">N</Emphasis>-(5-Methylisoxazol-3-yl) Benzenesulfonamide

Abstract  

Schiff base 4-[(2-hydroxy-3-methoxybenzylideneamino)-N-(5-methylisoxazol-3-yl)benzene-sulfonamide has been synthesized from the reaction of 4-amino-N-(5-methylisoxazol-3-yl)benzenesulfonamide(sulfamethoxazole) with 2-hydroxy-3-methoxybenzaldehyde. It has been characterized by elemental analysis, MS, IR, ¹H NMR, ¹³C NMR, HETCOR and UV–Visible techniques. The structure of it also has been examined crystallographically. For the compound exist as dominant form of enol-imines in both the solid state and the solutions. It crystallizes in the monoclinic space group P2₁/c with a = 8.2694(7), b = 8.3453(5), c = 26.260(2) ?, β = 97.142(7) °, V = 1798.1(2) ?³, D _x  = 1.431 g cm⁻³, R ₁ = 0.0529 and wR ₂ = 0.1370 [I > 2σ(I)], respectively.     

Synthesis,Spectroscopic Studies and Structure of 2-[(Benzo[<Emphasis Type="Italic">d</Emphasis>]thiazol-2-ylamino)methyl]phenol

Abstract  

Schiff base (E)-2-[(benzo[d]thiazol-2-ylimino)methyl]phenol (1) has been synthesized from the reaction of 2-hydroxy-benzaldehyde with 2-aminobenzothiazole. The 2-[(benzo[d]thiazol-2-ylamino)methyl]phenol (2) was prepared reduction of the Schiff base 1 with sodium borohydride. The compounds 1 and 2 have been characterized by elemental analysis, FT-IR, ¹H-NMR, ¹³C-NMR and UV–visible spectroscopic techniques. The structure of the compound 2 has also been examined crystallographically. The compound 2 crystallizes in the monoclinic space group P2/c. The unit cell parameters were found as a = 10.017(1), b = 11.725(1), c = 10.341(1) ?, V = 1208.1(1) ?³, D _x = 1.409 g cm⁻³ and Z = 4. The crystal structure was solved by direct methods and refined by the full-matrix least squares method and found as R ₁ = 0.0308 and wR ₂ = 0.0818 for 2032 for the observed reflections [I > 2σ(I)].     

A unified three point approximating subdivision scheme

In this paper,we propose a three point approximating subdivision scheme,with three shape parameters,that unifies three different existing three point approximating schemes.Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed.The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.     

On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions

In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the corresponding unit timelike split quaternion. We give the characterizations of eigenvalues (complex or real) of a rotation matrix in Minkowski 3 space according to only first component of the corresponding quaternion. Moreover, we find that the casual characters of rotation axis depend only on first component of the corresponding quaternion. Finally, we give the way to generate an orthogonal basis for ${\mathbb{E}^{3}_{1}}$ by using eigenvectors of a rotation matrix.     

A uniform stability result for thermoelasticity of type III with boundary distributed delay

In this paper we consider a thermoelastic system of type III with boundary distributed delay. Under suitable assumption on the weight of the delay, we prove, using the energy method, that the damping effect through heat conduction given by Green and Naghdi's theory is still strong enough to uniformly stabilize the system even in the presence of time delay.     

Discrete-Time Pricing and Optimal Exercise of American Perpetual Warrants in the Geometric Random Walk Model

An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.     

On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions

The purpose of the paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ-convergence of sequences of fuzzy numbers. We establish some connections between these concepts. It is also shown that if a sequence of fuzzy numbers is strongly almost λ-convergent with respect to a sequence of Orlicz funtions then it is almost λ-statistical convergent.