Journal Vol – 18 No -4, April 2023

Abstract:

In this paper, the author studied the skeletal congruences θ^* of a distributive nearlattice S, where * represents the pseudocomplement. Then the author described θ(I)^*, where θ(I) is the smallest congruence of S containing n-ideal I as a class and showed that I^+ is the n-kernel of θ(I)^*. In this paper, the author established the following fundamental results: When n is an upper element of a distributive nearlattice S, the author has shown that the n-kernels of the skeletal congruences are precisely those n-ideals which are the intersection of relative annihilator ideals and dual relative annihilator ideals whose endpoints are of the form x∨n and x∧n respectively. For a central element n of a distributive nearlattice S, the author proved that P_n (S) is disjunctive if and only if the n-kernel of each skeletal congruence is an annihilator n-ideal. Finally, the author discussed that P_n (S) is semi-Boolean if and only if the map θ→Ker_n θ is a lattice isomorphism of SC(S) onto K_n SC(S) whose inverse is the map I→θ(I) where I is an n-ideal and n is a central element of S.

Keywords:

n-Kernels of skeletal congruence,Pseudo complement,Annihilator n-ideal,Disjunctive nearlattice,Semi-Boolean algebra,

Refference:

I. A. S. A. Noor and M. B. Rahman, Congruence relations on a distributive nearlattice, Rajshahi University Studies Part-B, Journal of Science, 23-24(1995-1996) 195-202.
II. A. S. A. Noor and M. B. Rahman, Sectionally semicomplemented distributive nearlattices, SEA Bull. Math., 26(2002) 603-609.
III. M. A. Latif, n-ideals of a lattice, Ph.D. Thesis, Rajshahi University, Rajshahi, 1997.
IV. S. Akhter, Disjunctive Nearlattices and Semi-Boolean Algebras, Journal of Physical Sciences, Vol. 16, (2012), 31-43.
V. S. Akhter, A study of Principal n-Ideals of a Nearlattice, Ph.D. Thesis, Rajshahi University, Rajshahi, 2003.
VI. S. Akhter and M. A. Latif, Skeletal congruence on a distributive nearlattice, Jahangirnagar University Journal of Science, 27(2004) 325-335.
VII. S. Akhter and A. S. A. Noor, n-Ideals of a medial nearlattice, Ganit J. Bangladesh Math. Soc., 24(2005) 35-42.
VIII. W. H. Cornish, The Kernels of skeletal congruences on a distributive lattice, Math. Nachr., 84(1978) 219-228.
IX. W. H. Cornish and Hickman, Weakly distributive semilattice, Acta. Math. Acad. Sci. Hunger, 32(1978) 5-16.

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Abstract:

This paper proposes an additive watermarking on sparse or compressible coefficients of the host image in the presence of blurring and additive noise degradation. The sparse coefficients are obtained through basis pursuit (BP). Watermark recovery is done through deblurring, and performance is studied here for Wiener and fast total variation deconvolution (FTVD) techniques; the first one needs the actual or an estimate of the noise variance, while the second one is blind. Extensive simulations are done on images for different CS measurements along with a wide range of noise variations. Simulation results show that FTVD with an optimum value for regularization parameter enables the extraction of the watermark image in visually recognizable form, while Wiener deconvolution neither restores the watermarked image nor the watermark when no knowledge of noise is used.

Keywords:

Basis pursuit,CS imaging,additive watermarking,Wiener deblurring;,FTVD,

Refference:

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XV. P. Sen and S. Darabi, “A novel framework for imaging using compressed sensing,” in 16th IEEE International Conference on Image Processing (ICIP), Nov 2009, pp. 2133–2136.
XVI. Q. Wang, W. Zeng, and J. Tian, “A compressive sensing based secure watermark detection and privacy preserving storage framework,” IEEE Transactions on Image Processing, vol. 23, no. 3, pp. 1317–1328, March 2014.
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XX. S. S. Chen, D. L. Donoho, Michael, and A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Journal on Scientific Computing, vol. 20, pp. 33–61, 1998.
XXI. W. Lu and N. Vaswani, “Modified basis pursuit denoising(modifiedbpdn) for noisy compressive sensing with partially known support,” in IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), March 2010, pp. 3926–3929.
XXII. Y. Jiang and X. Yu, “On the robustness of image watermarking via compressed sensing,” in International Conference on Information Science, Electronics and Electrical Engineering (ISEEE), vol. 2, April 2014, pp. 963–967.
XXIII. Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM Journal of Imging Science, vol. 1, no. 3, pp. 248–272, 2008.

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Abstract:

In this study, the assessment of major factors that directly impact the success of the Industry 4.0 integration of the supply chain in terms of tangible and intangible business resources as well as the mediating role of work engagement over these business resources was performed. A total of 685 survey questions were distributed to voluntary participants in the supply chain management industry and 182 responses were studied. Structural Equation Modelling using AMOS software was carried out. Analysis such as variables and their related measurement scales, data screening, replacing missing values, removing outliers and testing normality of data, Harman’s single-factor test, and Confirmatory Factor Analysis were conducted. Descriptive results of the constructs were discussed.

Keywords:

Supply Chain Management,Industry 4.0,Business Resources,Structural Equation Modelling,

Refference:

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Abstract:

According to Pythagoras Theorem : In a right-angled triangle x² + y² = z² , where, base = x, altitude = y, and hypotenuse = z. In the present paper, the author states that x² + y² = – z² is the extended form of the Pythagoras Theorem.

Keywords:

Countup and countdown straight line,circle,Dynamics of Numbers,Pythagoras Theorem,

Refference:

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XIII. Prabir Chandra Bhattacharyya, ‘AN INTRODUCTION TO RECTANGULAR BHATTACHARYYA’S CO-ORDINATES: A NEW CONCEPT’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, November (2021). pp 76-86.
XIV. Prabir Chandra Bhattacharyya, ‘AN INTRODUCTION TO THEORY OF DYNAMICS OF NUMBERS: A NEW CONCEPT’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, January (2022). pp 37-53.
XV. Prabir Chandra Bhattacharyya, ‘A NOVEL CONCEPT IN THEORY OF QUADRATIC EQUATION’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-3, March (2022) pp 41-63.
XVI. Prabir Chandra Bhattacharyya. ‘A NOVEL METHOD TO FIND THE EQUATION OF CIRCLES’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-6, June (2022) pp 31-56
XVII. Prabir Chandra Bhattacharyya, ‘AN OPENING OF A NEW HORIZON IN THE THEORY OF QUADRATIC EQUATION: PURE AND PSEUDO QUADRATIC EQUATION – A NEW CONCEPT’. J. Mech. Cont. & Math. Sci., Vol.-17, No.-11, November (2022) pp 1-25.
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XX. S. Mahmud, (2019). Calculating the area of the Trapezium by Using the Length of the Non Parallel Sides: A New Formula for Calculating the area of Trapezium. International Journal of Scientific and Innovative Mathematical Research, volume 7, issue 4, pp.25-27.http://dx.doi.org/10.20431/2347-3142.0704004
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XXIII. THE APPLICATION OF CIRCLE EQUATION IN BUILDING COMPOSITEFRONTAGE. Advances in Mathematics: Scientific Journal 10 (2021), no.1, 29–35. https://doi.org/10.37418/amsj.10.1.4

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