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Regular Elements of &Lt;i>Bx(D) Defined by the Class ∑1(X,10)-&Lt;i>I

Applied Mathematics

doi 10.4236/am.2016.79078

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January 1, 2016

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Scientific Research Publishing, Inc.

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Regular Elements and Right Units of Semigroup &Lt;i>Bx(D) Defined Semilattice &Lt;i>D For Which &Lt;i>V(D,а)=Q ∈ &Amp;sum;3(X,8)

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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>

Applied Mathematics

doi 10.4236/am.2016.79078

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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)

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

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

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

On the Solutions of the Equation &Lt;i>x</I><sup>3</Sup> + &Lt;i>Ax</I> = &Lt;i>B</I> In &Lt;span Style="font-Family: Euclid Math Two">Z</Span><sub>3</Sub><sup Style="margin-Left:-6px;">*</Sup> With Coefficients From &Lt;span Style="font-Family: Euclid Math Two">Q</Span><sub>3</Sub>

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Comparison of Textural Characteristics of Ceria Solids Prepared via Triton X Reverse Micelles and &Lt;i>in Situ</I> Synthesized Ce(O<sup>i</Sup>Pr)<sub>4</Sub> And Ce(O<sup>i</Sup>Pr) &Lt;sub>3</Sub> Precursors

Amanote Research

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;

Applied Mathematics

doi 10.4236/am.2016.79078

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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)

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

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

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

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;

Comparison of Textural Characteristics of Ceria Solids Prepared via Triton X Reverse Micelles and &Lt;i&gt;in Situ&lt;/I&gt; Synthesized Ce(O&lt;sup&gt;i&lt;/Sup&gt;Pr)&lt;sub&gt;4&lt;/Sub&gt; And Ce(O&lt;sup&gt;i&lt;/Sup&gt;Pr) &Lt;sub&gt;3&lt;/Sub&gt; Precursors

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)

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

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

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

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

Comparison of Textural Characteristics of Ceria Solids Prepared via Triton X Reverse Micelles and &Lt;i>in Situ</I> Synthesized Ce(O<sup>i</Sup>Pr)<sub>4</Sub> And Ce(O<sup>i</Sup>Pr) &Lt;sub>3</Sub> Precursors