Volume 13 | Issue 11 |

 Abstract

Nutrition plays a critical role in influencing the biological, mechanical, and clinical aspects of orthodontic treatment. Adequate intake of macro- and micronutrients supports bone remodeling, collagen synthesis, and periodontal health, facilitating efficient orthodontic tooth movement (OTM). Deficiencies in essential nutrients such as calcium, vitamin D, and trace minerals can delay tooth movement, increase root resorption risk, and compromise periodontal stability. Bioactive food components like omega-3 fatty acids and flavonoids exhibit anti-inflammatory and antioxidant effects, enhancing tissue healing and reducing orthodontic-induced inflammation. Dietary modifications, including a soft yet nutrient-dense diet, protect appliances while maintaining nutritional adequacy. Integrating nutritional counseling and digital dietary tracking into orthodontic practice optimizes treatment efficiency, reduces complications, and promotes long-term stability. Overall, nutritioncentered orthodontic care strengthens the biological foundation of tooth movement and enhances treatment outcomes.

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 Keywords

Orthodontic tooth movement, Nutrition, Bone remodeling, Micronutrients, Dietary counseling

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Creative Commons Attribution 4.0 and The Open Definition

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Vocabulary building forms the foundation of all language-learning processes. A rich and functional vocabulary not only determines one's linguistic competence but also influences cognitive growth, comprehension skills, and communicative performance. In the modern multilingual classroom, vocabulary learning has evolved from rote memorization to dynamic engagement through reading, contextual exposure, and technology-assisted practice. This study examines how systematic vocabulary enhancement strengthens overall language proficiency, especially for learners of English as a second or foreign language. Drawing upon current pedagogical research, it discusses approaches such as morphological awareness, corpus-based learning, and the integration of digital tools. The paper concludes that vocabulary instruction must be intentional, context-sensitive, and continuous to ensure lasting lexical development and communicative success.

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Vocabulary Acquisition, Language Learning, Lexical Development, English Proficiency, Contextual Learning, Reading Strategies, Technology in Education, Pedagogical Approaches, Cognitive Linguistics, Learner Autonomy.

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Creative Commons Attribution 4.0 and The Open Definition

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Skin disease has a high prevalence throughout the world. Scabies is one of the commonest dermatological conditions in the world. It is a parasitic skin infestation caused by a mite called Sarcoptes scabiei var hominis. It is a highly contagious, neglected cutaneous parasitic disease, associated with poor individual, community, environmental circumstances and health. It Can be correlated to "Pama" as described in Ayurveda Classics. Pama Is one of the eighteen types of Kushta which is caused by Kapha Pitta Dosha. Scabies was added to the World Health Organization's (WHO) list of neglected tropical diseases In 2013. The present case shows the effect of Ayurvedic Formulation on scabies in 11yr old child.

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Scabies, Pama, Kushta, Aarogyavardhini Vati

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Water has consistently functioned as one of the most potent symbols in literature, religion, and philosophy. From representing life and purity to embodying destruction and renewal, water serves as a complex cultural metaphor across civilizations. This article examines the symbolism of water by engaging with Muhammad Hussain Azad's Aab-e ?ay?t, Sufi mystical thought, Hindu sacred river traditions, and the Western literary canon, with particular emphasis on Shakespeare and T.S. Eliot. It argues that water functions as both an existential and spiritual motif, unifying aesthetic, theological, and ecological discourses.

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Creative Commons Attribution 4.0 and The Open Definition

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Water symbolism, Urdu literature, Sufism, Hindu sacred rivers, purification, immortality, environmental humanities

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Creative Commons Attribution 4.0 and The Open Definition

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Diophantine equations of higher degrees, play a meaningful role in generating special elliptic curves that are crucial for cryptography and secure communications. In this paper, I was focused given Diophantine equation with more than 8 unknowns and focused on a study to find integer design of solutions Diophantine Equation ?(X^4+Y^4 )^2 (3U^2+V^2 )=T^2 (C^2+D^2 )(Z^2+W^2 ) P^? With ?>0,?=2,3,?=1,2,3,4,5,6,7 and x

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Creative Commons Attribution 4.0 and The Open Definition

 Keywords

Diophantine Equation, exponential, Pythagorean triplet, Integer design.

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Creative Commons Attribution 4.0 and The Open Definition

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The rapid growth of the Internet of Things ) and smart devices is revolutionizing electronic commerce (e-commerce) by enabling seamless connectivity, personalization, and automation across the business ecosystem. IOT - integrated smart devices enhance customer experience, optimize supply chains, and provide data-driven insights for better decision-making. However, IOT adoption in ecommerce also raises concerns about cyber security, interoperability, and the ethical use of consumer data. This paper explores the technological foundations, applications, opportunities, and challenges of IOT in e-commerce, highlighting its trans formative role in shaping innovative business models and redefining customer engagement. It also examines future directions, emphasizing sustainability and secure digital transformation.

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Keywords:Internet of Things,Smart Devices,E- Commerce ,Digital Transformation, Supply Chain

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Creative Commons Attribution 4.0 and The Open Definition

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This paper focused on a study to find integer design of solutions Diophantine Equation ?(X^4+Y^4 )(?U^2+V^2 )=T^2 (C^2-D^2 )(Z^2-W^2 ) P^? With ?>0,?>0 and X0,?>0 and X2 is parameterized by integers k and n, with variables defined as: x = k^n,y=k^(n+1),z=k^(n+3),w=k^(n+2),p=k^n, U=2^(n+1), V=2^n , T=3(2)^n , ?=(1+k^4 )(k^6-k^4 ) k^(?-2)n n^2 , and {?(C=(((1+k^4)/2)^2+1)n,D=(((1+k^4)/2)^2-1)n, if 1+k^4 is even@C=(((1+k^4 )^2+1)/2) )n,D=(((1+k^4 )^2-1)/2)n, if 1+k^4 is odd)}. for ?=1 is x = k^n,y=k^(n+1),z=k^(n+3),w=k^(n+2),p=k^2n,U=2^(n+1),V=2^n ,T=3(2)^n , ?=(1+k^4 )(k^6-k^4 ) n^2 and {?(C=(((1+k^4)/2)^2+1)n,D=(((1+k^4)/2)^2-1)n, if 1+k^4 is even@C=(((1+k^4 )^2+1)/2) )n,D=(((1+k^4 )^2-1)/2)n, if 1+k^4 is odd)}. for ?=2 is x = k^n,y=k^(n+1),z=k^(n+3),w=k^(n+2),p=k^n,U=2^(n+1),V=2^n ,T=3(2)^n , ?=(1+k^4 )(k^6-k^4 ) n^2 and {?(C=(((1+k^4)/2)^2+1)n,D=(((1+k^4)/2)^2-1)n, if 1+k^4 is even@C=(((1+k^4 )^2+1)/2) )n,D=(((1+k^4 )^2-1)/2)n, if 1+k^4 is odd)}. Lemma 2: At ?=3, the Diophantine equation ?(X^4+Y^4 )(3U^2+V^2 )=T^2 (C^2-D^2 )(Z^2-W^2 ) P^? With ?>0,?>0 and X2 is parameterized by integers k and n, with variables defined as: x = k^n,y=k^(n+1),z=k^(n+3),w=k^(n+2),p=k^n, U=3^n, V=3^n , T=2(3)^n , ?=(1+k^4 )(k^6-k^4 ) k^(?-2)n n^2 , and {?(C=(((1+k^4)/2)^2+1)n,D=(((1+k^4)/2)^2-1)n, if 1+k^4 is even@C=(((1+k^4 )^2+1)/2) )n,D=(((1+k^4 )^2-1)/2)n, if 1+k^4 is odd)}. for ?=1 is x = k^n,y=k^(n+1),z=k^(n+3),w=k^(n+2),p=k^2n,U=3^n, V=3^n , T=2(3)^n , ?=(1+k^4 )(k^6-k^4 ) n^2 and {?(C=(((1+k^4)/2)^2+1)n,D=(((1+k^4)/2)^2-1)n, if 1+k^4 is even@C=(((1+k^4 )^2+1)/2) )n,D=(((1+k^4 )^2-1)/2)n, if 1+k^4 is odd)}. for ?=2 is x = k^n,y=k^(n+1),z=k^(n+3),w=k^(n+2),p=k^n,U=3^n, V=3^n , T=2(3)^n , ?=(1+k^4 )(k^6-k^4 ) n^2 and {?(C=(((1+k^4)/2)^2+1)n,D=(((1+k^4)/2)^2-1)n, if 1+k^4 is even@C=(((1+k^4 )^2+1)/2) )n,D=(((1+k^4 )^2-1)/2)n, if 1+k^4 is odd)}

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Creative Commons Attribution 4.0 and The Open Definition

 Keywords

Diophantine Equation, exponential, Pythagorean triplet, Integer design.

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Creative Commons Attribution 4.0 and The Open Definition

 Abstract

Abstract: Diophantine equations of higher degrees, play a meaningful role in generating special elliptic curves that are crucial for cryptography and secure communications. In this paper, I was focused given Diophantine equation with more than 8 unknowns and focused on a study to find integer design of solutions Diophantine Equation ?(X^4+Y^4 )^2 (3U^2+V^2 )=T^2 (C^2+D^2 )(Z^2-W^2 ) P^? With ?>0,?=2,3,?=1,2,3,4,5,6,7 and x

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Creative Commons Attribution 4.0 and The Open Definition

 Keywords

Diophantine Equation, exponential, Pythagorean triplet, Integer design.

  License

Creative Commons Attribution 4.0 and The Open Definition

 Abstract

Diophantine equations of higher degrees, play a meaningful role in generating special elliptic curves that are crucial for cryptography and secure communications. In this paper, I was focused given Diophantine equation with more than 8 unknowns and focused on a study to find integer design of solutions Diophantine Equation ?(X^4+Y^4 )^2 (2U^2+V^2 )=T^2 (C^2+D^2 )(Z^2+W^2 ) P^? With ?>0,?=2,3,?=1,2,3,4,5,6,7 and x

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Creative Commons Attribution 4.0 and The Open Definition

 Keywords

Diophantine Equation, exponential, Pythagorean triplet, Integer design

  License

Creative Commons Attribution 4.0 and The Open Definition

 Abstract

Diophantine equations of higher degrees, play a meaningful role in generating special elliptic curves that are crucial for cryptography and secure communications. In this paper, I was focused given Diophantine equation with more than 8 unknowns and focused on a study to find integer design of solutions Diophantine Equation ?(X^4+Y^4 )^2 (2U^2+V^2 )=T^2 (C^2+D^2 )(Z^2-W^2 ) P^? With ?>0,?=2,3,?=1,2,3,4,5,6,7 and x

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Creative Commons Attribution 4.0 and The Open Definition

 Keywords

Diophantine Equation, exponential, Pythagorean triplet, Integer design

  License

Creative Commons Attribution 4.0 and The Open Definition