(PDF) Regular Elements of the Semigroup

Regular Elements of the Semigroup &Lt;i>B X &Lt;/Sub> (&Lt;i>D) Defined by Semilattices of the Class &Amp;Sigma;2 (&Lt;i>X, 8) and Their Calculation Formulas

Applied Mathematics

doi 10.4236/am.2015.614199

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Date

January 1, 2015

Authors

Nino Tsinaridze

Shota Makharadze

Guladi Fartenadze

Publisher

Scientific Research Publishing, Inc.

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Regular Elements of the Semigroup &Lt;i>B</I><sub> X &Lt;/Sub> (&Lt;i>D</I>) Defined by Semilattices of the Class &Amp;Sigma;<sub>2</Sub> (&Lt;i>X</I>, 8) and Their Calculation Formulas

Applied Mathematics

doi 10.4236/am.2015.614199

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Regular Elements of &Lt;i>B<sub>x</Sup></I>(D) Defined by the Class ∑<sub>1</Sub>(X,10)-&Lt;i>I</I>

Regular Elements and Right Units of Semigroup &Lt;i>B<sub>x</Sub></I>(<i>D</I>) Defined Semilattice &Lt;i>D</I> For Which &Lt;i>V</I>(<i>D</I>,а)=Q ∈ &Amp;sum;<sub>3</Sub>(<i>X</I>,8)

Ion Exchange of Layer-Structured Titanate Cs<sub>x</Sub>Ti<sub>2</Sub>-&Lt;i><sub>x</Sub></I>/&Lt;sub>2</Sub>Mg<i><sub>x</Sub></I>/&Lt;sub>2</Sub>O<sub>4</Sub> (&Lt;i>x</I> = 0.70) and Applications as Cathode Materials for Both Lithium- And Sodium-Ion Batteries

Structural and Morphological Study of a Series of Ball Milled Nanocrystalline Fe<sub>1-&Lt;i>x</I></Sub>Al<sub><i>x</I></Sub> (0.3 ≤ &Lt;i>x</I> ≤ 0.6) Alloys

Synthesis of Hollow Nanoparticles &Lt;i>γ</I>-Al<sub>2</Sub>O<sub>3</Sub>

Detailed Analysis of Five Aspects Addressed to Minimize Costs and Waste in the Chemical Bath Deposition of CdS Films Using the Cd<i>B</I>–<i>A</I>C<sub>6</Sub>H<sub>5</Sub>O<sub>7</Sub>–<i>A</I>OH–(NH<sub>2</Sub>)<sub>2</Sub>CS System

Solutions of the Exponential Equation &Lt;i>y</I><sup><i>x/Y</I></Sup> = &Lt;i>x</I> Or Ln<i>x</I>/&Lt;i>x</I> = Ln<i>y</I>/&Lt;i>y</I> And Fine Structure Constant

Perfluorocyclobutane (PFC-318, &Lt;i>c</I>-C<sub>4</Sub>F<sub>8</Sub>) in the Global Atmosphere

Bringing Back the Body Into Positive Psychology: The Theory of &Lt;i>Corporeal</I> &Lt;i>Posttraumatic</I> &Lt;i>Growth</I> &Lt;i>in</I> &Lt;i>Breast</I> &Lt;i>Cancer</I> &Lt;i>Survivorship</I>

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Regular Elements of the Semigroup &Lt;i&gt;B&lt;/I&gt;&lt;sub&gt; X &Lt;/Sub&gt; (&Lt;i&gt;D&lt;/I&gt;) Defined by Semilattices of the Class &Amp;Sigma;&lt;sub&gt;2&lt;/Sub&gt; (&Lt;i&gt;X&lt;/I&gt;, 8) and Their Calculation Formulas

Applied Mathematics

doi 10.4236/am.2015.614199

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Abstract

Date

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Regular Elements of &Lt;i&gt;B&lt;sub&gt;x&lt;/Sup&gt;&lt;/I&gt;(D) Defined by the Class ∑&lt;sub&gt;1&lt;/Sub&gt;(X,10)-&Lt;i&gt;I&lt;/I&gt;

Regular Elements and Right Units of Semigroup &Lt;i&gt;B&lt;sub&gt;x&lt;/Sub&gt;&lt;/I&gt;(&lt;i&gt;D&lt;/I&gt;) Defined Semilattice &Lt;i&gt;D&lt;/I&gt; For Which &Lt;i&gt;V&lt;/I&gt;(&lt;i&gt;D&lt;/I&gt;,а)=Q ∈ &Amp;sum;&lt;sub&gt;3&lt;/Sub&gt;(&lt;i&gt;X&lt;/I&gt;,8)

Structural and Morphological Study of a Series of Ball Milled Nanocrystalline Fe&lt;sub&gt;1-&Lt;i&gt;x&lt;/I&gt;&lt;/Sub&gt;Al&lt;sub&gt;&lt;i&gt;x&lt;/I&gt;&lt;/Sub&gt; (0.3 ≤ &Lt;i&gt;x&lt;/I&gt; ≤ 0.6) Alloys

Synthesis of Hollow Nanoparticles &Lt;i&gt;γ&lt;/I&gt;-Al&lt;sub&gt;2&lt;/Sub&gt;O&lt;sub&gt;3&lt;/Sub&gt;

Solutions of the Exponential Equation &Lt;i&gt;y&lt;/I&gt;&lt;sup&gt;&lt;i&gt;x/Y&lt;/I&gt;&lt;/Sup&gt; = &Lt;i&gt;x&lt;/I&gt; Or Ln&lt;i&gt;x&lt;/I&gt;/&Lt;i&gt;x&lt;/I&gt; = Ln&lt;i&gt;y&lt;/I&gt;/&Lt;i&gt;y&lt;/I&gt; And Fine Structure Constant

Perfluorocyclobutane (PFC-318, &Lt;i&gt;c&lt;/I&gt;-C&lt;sub&gt;4&lt;/Sub&gt;F&lt;sub&gt;8&lt;/Sub&gt;) in the Global Atmosphere

Bringing Back the Body Into Positive Psychology: The Theory of &Lt;i&gt;Corporeal&lt;/I&gt; &Lt;i&gt;Posttraumatic&lt;/I&gt; &Lt;i&gt;Growth&lt;/I&gt; &Lt;i&gt;in&lt;/I&gt; &Lt;i&gt;Breast&lt;/I&gt; &Lt;i&gt;Cancer&lt;/I&gt; &Lt;i&gt;Survivorship&lt;/I&gt;

Regular Elements of the Semigroup &Lt;i>B</I><sub> X &Lt;/Sub> (&Lt;i>D</I>) Defined by Semilattices of the Class &Amp;Sigma;<sub>2</Sub> (&Lt;i>X</I>, 8) and Their Calculation Formulas

Regular Elements of &Lt;i>B<sub>x</Sup></I>(D) Defined by the Class ∑<sub>1</Sub>(X,10)-&Lt;i>I</I>

Regular Elements and Right Units of Semigroup &Lt;i>B<sub>x</Sub></I>(<i>D</I>) Defined Semilattice &Lt;i>D</I> For Which &Lt;i>V</I>(<i>D</I>,а)=Q ∈ &Amp;sum;<sub>3</Sub>(<i>X</I>,8)

Structural and Morphological Study of a Series of Ball Milled Nanocrystalline Fe<sub>1-&Lt;i>x</I></Sub>Al<sub><i>x</I></Sub> (0.3 ≤ &Lt;i>x</I> ≤ 0.6) Alloys

Synthesis of Hollow Nanoparticles &Lt;i>γ</I>-Al<sub>2</Sub>O<sub>3</Sub>

Solutions of the Exponential Equation &Lt;i>y</I><sup><i>x/Y</I></Sup> = &Lt;i>x</I> Or Ln<i>x</I>/&Lt;i>x</I> = Ln<i>y</I>/&Lt;i>y</I> And Fine Structure Constant

Perfluorocyclobutane (PFC-318, &Lt;i>c</I>-C<sub>4</Sub>F<sub>8</Sub>) in the Global Atmosphere

Bringing Back the Body Into Positive Psychology: The Theory of &Lt;i>Corporeal</I> &Lt;i>Posttraumatic</I> &Lt;i>Growth</I> &Lt;i>in</I> &Lt;i>Breast</I> &Lt;i>Cancer</I> &Lt;i>Survivorship</I>