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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:

I. E. Candès, N. Braun, and M. Wakin, “Sparse signal and image recovery from compressive samples,” in 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI, April 2007, pp. 976–979.
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III. F. Lin and C. Jin, “An improved wiener deconvolution filter for highresolution electron microscopy images,” Micron, vol. 50, no. 0, pp. 1 – 6, 2013.
IV. H.-C. Huang, F.-C. Chang, C.-H. Wu, and W.-H. Lai, “Watermarking for compressive sampling applications,” in Eighth International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP),, July 2012, pp. 223–226.
V. H. Liao, F. Li, and M. K. Ng, “Selection of regularization parameter in total variation image restoration,” Journal of the Optical Society of America A, vol. 26, no. 11, pp. 2311–2320, Nov 2009.
VI. H. W. Engl and W. Grever, “Using the l-curve for determining optimal regularization parameters,” Numerical Mathematics, vol. 69, no. 1, pp. 25–31, 1994.
VII. I. Orovic and S. Stankovic, “Combined compressive sampling and image watermarking,” in 55th International Symposium ELMAR, Sept 2013, pp. 41–44.
VIII. J. Ma and F.-X. Le Dimet, “Deblurring from highly incomplete measurements for remote sensing,” IEEE Transactions on Geoscience and Remote Sensing, vol. 47, no. 3, pp. 792–802, March 2009.
IX. J. Romberg, “Imaging via compressive sampling [introduction to compressive sampling and recovery via convex programming],” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 14–20, 2008.
X. J. Yang, J. Wright, T. S. Huang, and Y. Ma, “Image super-resolution via sparse representation,” IEEE Transactions on Image Processing, vol. 19, no. 11, pp. 2861–2873, 2010.
XI. L. Ruidong, S. She, Z. Hongtai, T. Xiaomin, and Z. Lanlan, “Analysis on the affection of noise in radar super resolution though deconvolution,” in IET International Radar Conference, April 2009, pp. 1–4.
XII. L. Spinoulas, B. Amizic, M. Vega, R. Molina, and A. Katsaggelos, “Simultaneous bayesian compressive sensing and blind deconvolution,” in Proceedings of the 20th European Signal Processing Conference (EUSIPCO), Aug 2012, pp. 1414–1418.
XIII. M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 83–91, March 2008.
XIV. P. Samarasinghe, R. Kennedy, and H. Li, “On non-blind image restoration,” in 3rd International Conference on Signal Processing and Communication Systems, ICSPCS, Sept 2009, pp. 1–7.
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.
XVII. R. C. Gonzalez and R. E. Woods, Digital Image Processing (3rd Edition). Upper Saddle River, NJ, USA: Prentice-Hall, Inc., 2006.
XVIII. S. Babacan, R. Molina, and A. Katsaggelos, “Variational bayesian blind deconvolution using a total variation prior,” IEEE Transactions on Image Processing, vol. 18, no. 1, pp. 12–26, Jan 2009.
XIX. S. Cho, J. Wang, and S. Lee, “Handling outliers in non-blind image deconvolution,” in IEEE International Conference on Computer Vision (ICCV), Nov 2011, pp. 495–502.
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:

I. Awang, Z. (2012). Structural equation modeling using AMOS graphic: Penerbit Universiti Teknologi MARA B.
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IV. Barney, J.B. (1997): Gaining and sustaining competitive advantage. Reading: Addison- Wesley.
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VIII. Cater,T. And Cater B. (2009). (In)tangible resources as antecedents of a company’s competitive advantage and performance, Journal for East European Management Studies, 14(2), 186-209.
IX. Coffman, D. L., & Maccallum, R. C. (2005). Using parcels to convert path analysis models into latent variable models. Multivariate Behavioral Research, 40(2), 235-259.
X. Cohen, J., and Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences 2nd Ed.. Hillsdale, NJ: Erlbaum
XI. Collier, N., Fishwick, F. and Floyd, S.W. (2004), “Managerial involvement and perceptions of
XII. strategy process”, Long Range Planning, Vol. 37 No. 1, pp. 67-83.
XIII. DeVellis, R. F. (2011). Scale development: Theory and applications (Vol. 26): Sage Publications
XIV. Gates, D. (2017). Industry 4.0: scaling up to success. Retrieved from https://assets.kpmg.com/content/dam/kpmg/xx/pdf/2017/04/industry-4-scaling-up-to-success.pdf
XV. Fornell, C. and Larcker, D.F. (1981) ‘Evaluating structural equation models with unobservable variables and measurement error’, Journal of Marketing Research, Vol. 18, No. 1, pp.39–50.
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XVII. Graham, J. W., S. M. Hofer, S. L. Donaldson, D. P. MacKinnon, and J. L. Schafer. (1997). Analysis with missing data in prevention research. In The science of prevention: Methodological advances from alcohol and substance abuse research, ed. K. Bryant, M. Windle and S. West, 325-366. Washington, DC: American Psychological Association.
XVIII. Hair, J. F., Thomas, G., Hult, M., Ringle, C. M., & Sarstedt, M. (2017). A Primer on Partial Least Squares Structural Equation Modeling (2nd ed.). Thousand Oakes, CA: Sage
XIX. Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2006). Multivariate data analysis (sixth ed.). United State of Amreica: Pearson prentice hall.
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XXI. Hair Jr, J. F., Anderson, R. E., Tatham, R. L., & William, C. (1995). Black (1995), Multivariate data analysis with readings. New Jersy: Prentice Hall.
XXII. Hoyle, R.H. (1995) The Structural Equation Modeling Approach: Basic Concepts and Fundamental Issues, Sage, Thousand Oaks, CA.
XXIII. Kline, T. J. (2005). Psychological testing: A practical approach to design and evaluation. Sage publications.
XXIV. Kline, R. B. (2010). Principles and practice of structural equation modeling: The Guilford Press
XXV. Kohtamäki, M., Kraus, S., Mäkelä, M., & Rönkkö, M. (2012). The role of personnel commitment to strategy implementation and organisational learning within the relationship between strategic planning and company performance. International Journal of Entrepreneurial Behavior & Research, 18(2), 159-178.
XXVI. Lobo, A. F. (2020, March 16). Industry 4.0: Can We Rescue It From Failure? Retrieved from https://www.forbes.com/sites/forbestechcouncil/2020/03/16/industry-4-0-can-we-rescue-it-from-failure/?sh=5eb372036ba4
XXVII. Milliken, A. L. (2012). The Importance of Change Management in Supply Chain. Journal of Business Forecasting, 31(2).
XXVIII. Nunnally, J.C. and Bernstein, I.H. (1994) Psychometric Theory, McGraw-Hill, New York.
XXIX. Podsakoff, P. M., MacKenzie, S. B., Lee, J.-Y., & Podsakoff, N. P. (2003). Common method biases in behavioral research: a critical review of the literature and recommended remedies. Journal of applied psychology, 88(5), 879.
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XXXI. Ruessmann, M., M. Lorenz, P. Gerbert, M. Waldner, J. Justus, P. Engel and M. Harnisch. Industry 4.0: The Future of Productivity and Growth in Manufacturing Industries, Boston Consulting Group, 2015.
XXXII. Salkin, C., Oner, M., Ustundag, A., & Cevikcan, E. (2018). A conceptual framework for Industry 4.0. Industry 4.0: managing the digital transformation, 3-23
XXXIII. Schaufeli, W. B., & Bakker, A. B. (2004). Job demands, job resources, and their relationship with burnout and engagement: A multi‐sample study. Journal of Organizational Behavior: The International Journal of Industrial, Occupational and Organizational Psychology and Behavior, 25(3), 293-315.
XXXIV. Shoshanah, C., & Roussel, J. (2005). Strategic Supply Chain Management: The Five Disciplines For Top Performance
XXXV. Stentoft, J., Wickstrom, K.A., Philipsen, K. ve Haug, A.(2019). Drivers and Barriers for Industry 4.0 Readiness and Practice: A SME Perspective with Empirical Evidence, Proceedings of the 52nd Hawaii International Conference on System Sciences, 5155-5164
XXXVI. Tabachnick B. G. ve Fidell, L. S. (2011). Using multivariate statistics, 6th edition, Pearson, U.S.A.
XXXVII. Tajri, H., & Chafi, A. (2018, April). Change management in supply chain. In 2018 4th International Conference on Optimization and Applications (ICOA) (pp. 1-6). IEEE
XXXVIII. Zhou, K.Z. and Wu, F. (2010). Technological capability, strategic flexibility, and product innovation, Strategic Management Journal, 31, 547-561

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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:

I. A. VASSILIOU: Mathematics in Europe: Common challenges and national policies. Brussels: Education, Audiovisual and Culture Executive Agency, [Online], Available: http://eacea.ec.europa.eu/0Aeducation/eurydice/documents/thematic_reports/132EN.pdf[12], (2011).
II. B. Kaushik, (2015). “A New and Very Long Proof of the Pythagoras Theorem By Way of a Proposition on Isosceles Triangles,” MPRA Paper 61125, University Library of Munich, Germany. https://ideas.repec.org/p/pra/mprapa/61125.html
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IV. E. J. Barbeau, Pell’s Equation, Springer-Verlag, NY, 2003
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VI. F. Bernhart and H. Lee Price, On Pythagorean Triples I, preprint
VII. F. J. M. Barning, On Pythagorean and quasi-Pythagorean triangles and a generation process with the help of unimodular matrices. (Dutch) Math. Centrum Amsterdam Afd. Zuivere Wisk. ZW-001 (1963).
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IX. HOSSEINALI GHOLAMI, AND MOHAMMAD HASSAN ABDUL SATHAR.
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XII. L. Nurul , H., D., (2017). Five New Ways to Prove a Pythagorean Theorem, International Journal of Advanced Engineering Research and Science, volume 4, issue 7, pp.132-137 http://dx.doi.org/ 10.22161/ijaers.4.7.21
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.
XVIII. Prabir Chandra Bhattacharyya, ‘A NOVEL CONCEPT FOR FINDING THE FUNDAMENTAL RELATIONS BETWEEN STREAM FUNCTION AND VELOCITY POTENTIAL IN REAL NUMBERS IN TWO-DIMENSIONAL FLUID MOTIONS’. J. Mech. Cont. & Math. Sci., Vol.-18, No.-02, February (2023) pp 1-19
XIX. Salman Mahmud, 14 New Methods to Prove the Pythagorean Theorem by using Similar Triangles, International Journal of Scientific and Innovative Mathematical Research (IJSIMR), vol. 8, no. 2, pp. 22-28, 2020. Available : DOI: http://dx.doi.org/10.20431/2347-3142.0802003

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
XXI. S. Mahmud, (2019) A New Long Proof of the Pythagorean Theorem, International Journal of Scientific and Innovative Mathematical Research vol. 7, no. 9, pp. 3-7, 2019. DOI: http://dx.org/10.20431/2347- 3142.0709002
XXII. Swaminathan S (2014). The Pythagorean Theorem, Journal of Biodiversity, Bioprospecting and Development. vol.1, issue 3, doi :10.4172/2376-0214.1000128
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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