❙✉♠♠❛r2 ❚❤❡ ❋♦✉r✐❡r Ps❡✉❞♦s♣❡❝tr❛❧ ❚✐♠❡ ❉♦♠❛✐♥ ✭❋♦✉r✐❡r✲P❙❚❉✮ ♠❡t❤♦❞ ✇❛s s❤♦✇♥ t♦ ❜❡ ❛♥ ❡✛❡❝t✐✈❡ ✇❛2 ♦❢ ♠♦❞❡❧❧✐♥❣ ✇❛✈❡ ♣r♦♣❛❣❛t✐♦♥✳ ❋♦✉r✐❡r✲P❙❚❉ ✐s ❜❛s❡❞ ♦♥ ❋♦✉r✐❡r ❛♥❛❧2s✐s ❛♥❞ s2♥t❤❡s✐s t♦ ❝♦♠♣✉t❡ t❤❡ s♣❛t✐❛❧ ❞❡r✐✈❛t✐✈❡s ♦❢ t❤❡ ❣♦✈❡r♥✐♥❣ ✇❛✈❡ ❡q✉❛t✐♦♥✳ ❚❤❡r❡❢♦r❡✱ t❤❡ ♠❡t❤♦❞ s✉✛❡rs ❢r♦♠ t❤❡ ✇❡❧❧✲❦♥♦✇♥ ●✐❜❜s ♣❤❡♥♦♠❡♥♦♥ ✇❤❡♥ ❝♦♠♣✉t✐♥❣ ❛ ♥♦♥✲s♠♦♦t❤ ♦r ❞✐s❝♦♥t✐♥✉♦✉s ❢✉♥❝t✐♦♥✳ ❚❤✐s ❧✐♠✐ts ✐ts ♣♦ss✐...

Numer i ca l q u a n t i f i e r s p r o v i d e s imp le means o f f o r m a l i z i n g such s ta temen ts a s , " a t l e a s t t h r e e peop le a re i n t h a t r o o m " , " a t most f i f t e e n peop le a re i n the e l e v a t o r " , and "everybody has e x a c t l y two p a r e n t s " . A l t h o u g h n u m e r i c a l q u a n t i f i e r s g e n e r a l i z e the e x i s t e n t i ...

Simple sentences w i t h p l u r a l s have i n t e r p r e t a t i o n s t h a t cannot be reduced t o p r e d i c a t i o n s abou? i n d i v i d u a l o b j e c t s . Such an i n t e r p r e t a t i o n f o r a sentence w i t h 1 p l u r a l s cannot be represented by a l o q i c a l form c o n t a i n i n g q u a n t i f i e r s over i n d i v i d u a l s t h a t b i n d i n t o an atomic q...

subject to Gj(x, t) ≤ 0 for all t ∈ Tj , j ∈ q, Hk(x, s) = 0 for all s ∈ Sk, k ∈ r, x ∈ X, where q and r are positive integers, X is a nonempty open convex subset of Rn (n-dimensional Euclidean space), for each j ∈ q ≡ {1, 2, . . . , q} and k ∈ r, Tj and Sk are compact subsets of complete metric spaces, f and g are real-valued functions defined on X, for each j ∈ q, z → Gj(z, t) is a real-value...

We derive the full set of field equations for metric-affine version Myrzakulov gravity model and also extend this family theories to a broader one. More specifically, we consider whose gravitational Lagrangian is given by F(R,T,Q,T,D) where T, Q are torsion non-metricity scalars, T trace energy-momentum tensor D divergence dilation current. then linear case aforementioned theory and, assuming c...

For all 0 < t ≤ 1, we define a locally Euclidean metric ρt on R . These metrics are invariant under Euclidean isometries and, if t increases to 1, converge to the Euclidean metric dE . This research is motivated by expanding universe. key words. locally Euclidean metric PACS number(s). 98.80.Jk Mathematics Subject Classifications (2000). 85A40, 57M50 1 The metric ρt Let dE denote the Euclidean ...

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+1 → S2 of the form u(t, r) = Q(λ(t)r)+R(t, r) where u is the polar angle on the sphere, Q(r) = 2 arctan r is the ground state harmonic map, λ(t) = t−1−ν , and R(t, r) is a radiative error with local energy going to zero as t→ 0. The number ν > 1 2 can be described arbitrarily. This is accomplish...