... human evolution and expansion: (1) medium-sized mammalian herbivore availability; (2) terrain topography; (3) habitat and landscape structure and distribution; and (4) physical and ecological ... distance from source areas and mountain barriers, delaying access In the earlier colonisations 48 Neanderthals and Modern Humans only the Mediterranean and adjacent lands were colonised, the Plains ... heidelbergensis and H helmei would have been present in Europe at the same time (Foley & Lahr, 1997) and this was also the case between Modern Humans and Neanderthals Increasingly, frequent cold and arid...
... colon and a semi-colon in a list Punctuation of equations British and American English quotation marks IEEE and APA style reference format basics How to use an En dash (–) and an Em dash (—) Contractions ... h, reheated (121 °C for 30 min), and stored at °C for 3, 6, 12, and 24 h and 2, 4, 6, and days or -20, 4, and 20 °C for days A space between the numerical value and unit symbol even for degrees ... Teaching and Learning and Adam Turner Index to common punctuation errors The clause in English Using commas How to use a colon and a semi-colon in a list Punctuation of equations British and American...
... k(·)-contraction Assume that there exist x0 ∈ L and δ > such that d(x0 , T x0 ) ≤ αδ and sup k(t) < inf a(t), t∈(0,δ] t∈(0,δ] where λ ∈ (0, 1], a and k are the constant and the functions occuring in the definition ... R-function α : [0, ∞) → [0, 1) and L ≥ such that H(T x, T y) ≤ α(d(x, y))d(x, y) + Ld(y, T x) for all x, y ∈ X Mizoguchi–Takahashi’s type contractionsand Berinde–Berinde’s type contractions are relevant ... of X and the lower semicontinuity of f and p(u, ·), we know that (Y, d) is a nonempty complete metric space Applying a generalization version of Ekeland’s variational principle due to Lin and...
... /2} (3:11) and Let now α0 ∈ A and ε0 > be arbitrary and fixed, let n0 = max {n2(a0, ε0), n3(a0, ε0)} + and let k, l Î N be arbitrary and fixed such that k > l > n0 Then, k = i0 + n0 and l = j0 ... holds and, additionally, the conditions (D1) and (D3) hold, then (D2) is satisfied Włodarczyk and Plebaniak Fixed Point Theory and Applications 2011, 2011:90 http://www.fixedpointtheoryandapplications.com/content/2011/1/90 ... Î X and w Î X satisfy (Dl) By (6.1) and (D3), we have that w = T[q] (w) for some q Î N Next, by (C2) or (C3) or (C4) and by Proposition 3.4(d), Fix(T) = {w} and ∀α∈A {Jα (w, w) = 0} This and...
... k(·)-contraction Assume that there exist x0 ∈ L and δ > such that d(x0 , T x0 ) ≤ αδ and sup k(t) < inf a(t), t∈(0,δ] t∈(0,δ] where λ ∈ (0, 1], a and k are the constant and the functions occuring in the definition ... R-function α : [0, ∞) → [0, 1) and L ≥ such that H(T x, T y) ≤ α(d(x, y))d(x, y) + Ld(y, T x) for all x, y ∈ X Mizoguchi–Takahashi’s type contractionsand Berinde–Berinde’s type contractions are relevant ... of X and the lower semicontinuity of f and p(u, ·), we know that (Y, d) is a nonempty complete metric space Applying a generalization version of Ekeland’s variational principle due to Lin and...
... c l y, and d c t , c t of c forms a geodesic segment which joins x and y A geodesic triangle Δ x1 , x2 , x3 consists of three points x1 , x2 , and x3 in X the vertices of the triangle and three ... xn n→∞ 3.26 Fixed Point Theory and Applications Theorem 3.5 Let X be a complete CAT space and let K ⊆ X be nonempty, bounded, closed, and convex Let T : K → K and for n ∈ N, let αn : K → R be ... Kirk and H.-K Xu, “Asymptotic pointwise contractions, ” Nonlinear Analysis: Theory, Methods & Applications, vol 69, no 12, pp 4706–4712, 2008 N Hussain and M A Khamsi, “On asymptotic pointwise contractions...
... 1.3 Let T and I be self-mappings of a normed space X, S ⊂ X such that T(∂S) ⊂ S, and x ∈ F(T)∩F(I) Suppose T is I-nonexpansive on PS (x)∪{x}, I is linear and continuous on PS (x), and T and I are ... space X, and T and I continuous selfmappings of S such that T(S) ⊂ I(S) Suppose I is linear, p ∈ F(I), S is p-starshaped, and cl(T(S)) is compact If T and I are R-subweakly commuting and satisfy ... space X, and T and I continuous selfmappings of S such that T(S) ⊂ I(S) Suppose I is linear, p ∈ F(I), S is p-starshaped, and cl(T(S)) is compact If T and I are R-subweakly commuting and T is...
... 32 More about clauses We’ve looked at nouns, and the work they do, and at adjectives and adverbs and the work they Let’s go back now to clauses, and see how a whole clause can function like a ... something else to add to it, put a comma in and write the new bit, and then another comma and another new bit, and on we go Then when it looks long enough and has enough commas (or hyphens or other ... Page PART 2: Punctuation Preface: What this part is and isn’t 37 Intro 38 I’m writing ordinary sentences What punctuation marks I need? 40 What’s the difference between a hyphen and a dash? Aren’t...
... subjects and verbs Examples: I like cake and he likes ice cream Two pairs of subjects and verbs He and I like cake Two subjects and one verb She lifts weights and jogs daily One subject and two ... who and whom or they’re celebrating life in new and extraordinary ways because of our work together, it’s music to my ears and a gift to my spirit.’’ Foreword The Blue Book of Grammar andPunctuation ... plural verbs With or and nor With either and neither With conjunctions such as andand but With interrupting expressions With pronouns as subjects such as each, everyone, and anybody With portions...
... games, and quizzes log onto www.englishbanana.com now! Talk a Lot Foundation Course English Banana.com Lesson Page 15 Talk a Lot Foundation Course Lesson – List of Contractionsand Mega Contractions ... games, and quizzes log onto www.englishbanana.com now! Talk a Lot Foundation Course English Banana.com Lesson Page 16 Talk a Lot Foundation Course Lesson – List of Contractionsand Mega Contractions ... games, and quizzes log onto www.englishbanana.com now! Talk a Lot Foundation Course English Banana.com Lesson Page 17 Talk a Lot Foundation Course Lesson – List of Contractionsand Mega Contractions...
... is short, e.g travel, money, lover, and orange 72 English Banana.com Spelling Patterns and the Sounds they Make – Diphthongs are written with an r in the spelling There are 10 diphthongs in English ... only vowel digraph for oy, and ou is the only vowel digraph for au 74 English Banana.com Spelling Patterns and the Sounds they Make – Other consonant letters like w, y, and gh count as part of long ... spelled with the distinctive ee and oo patterns: Sound: Spelling Pattern: Example: More Examples: ee ee been _ oo oo cool _ Long vowel sounds ee and oo are sometimes represented...
... 88 UNIT Special Punctuation 90 33 Colons and Semicolons 90 34 Hyphens and Dashes 92 Units 5–8 Review: Punctuation in Context 100 Units 1–8 Review: Capitalization andPunctuation in Context ... ENGLISH iin n ccontext o n te x t CAPITALIZATION ANDPUNCTUATION GRAMMAR AND USAGE READING COMPREHENSION SPELLING VOCABULARY WRITING Development and Production: Laurel Associates, Inc Cover Art: ... Quotation Greetings and Closings in Letters 10 UNIT Names of Things 42 16 Brand Names 42 17 Organizations and Religions 44 18 Titles of Works 46 19 Days, Months, and Holidays 48 The...