robench-2024b
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48 items • Updated
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**A**: italic_c ( italic_x ) ∈ italic_B → caligraphic_P ( 1 ) end_ARG end_CELL end_ROW start_ROW start_CELL E-Fc) divide start_ARG italic_b ∈ italic_B italic_f ∈ italic_B → caligraphic_P ( 1 ) end_ARG start_ARG sansserif_Ap ( italic_f , italic_b ) ∈ caligraphic_P ( 1 ) end_ARG end_CELL start_CELL italic_β C-Fc) divide ... | CAB | CBA | BCA | ACB | Selection 3 |
**A**: ℱℱ{\mathcal{F}}caligraphic_F).
**B**: ε𝜀\varepsilonitalic_ε, N𝑁Nitalic_N) and growth functions (e.g**C**: The language of ultrafilters adds one more layer of notational complexity to an already notationally-intensive paper; however, there are gains to be made elsewhere, most notably in eliminating many quantit... | CBA | BAC | ABC | ACB | Selection 1 |
**A**: In Subsection 2.2, we show how to pass from a 2-automaton to a decorated graph. Finally in Subsection 2.3 we show how to turn a decorated graph into an admissible tree.
**B**: The reader interested in the motivation can jump directly to Subsection 2.2 and refer back as needed**C**: The structure of this section ... | ACB | ABC | CBA | BCA | Selection 3 |
**A**: On a given domain of the Euclidean space, the problem can be reduced to inverse coefficient problems for elliptic equations which were solved in [62].
We are concerned with the stability of the inverse problem.**B**: Generalizations and alternative methods to solve the problem have been studied in [3, 17, 42, 47... | ACB | ABC | BCA | CBA | Selection 4 |
**A**: Other rewriting algorithms also exist, for example Cohen et al. [26] present algorithms to compute with elements of finite Lie groups.
**B**: One important task in this context is writing elements of classical groups as words in standard generators using SLPs**C**: This is done in Magma [14] using the results of... | BCA | CBA | CAB | ACB | Selection 3 |
**A**: A polynomial P∈R𝑃𝑅P\in Ritalic_P ∈ italic_R is said to have a Jacobian mate**B**: Furthermore, by the sake of
simplicity we set R:=K[x,y]assign𝑅𝐾𝑥𝑦R:=K[x,y]italic_R := italic_K [ italic_x , italic_y ]**C**: 𝐰:=(w1,w2)assign𝐰subscript𝑤1subscript𝑤2\mathbf{w}:=(w_{1},w_{2})bold_w := ( italic_w start_POST... | CAB | CBA | BCA | BCA | Selection 2 |
**A**: This paper is a result of Thomas Geisser’s suggestion to consider a motivic version of Murre and H. Saito’s work on regular homomorphisms. As mentioned above, the referee’s contribution was enormous**B**: We would like to thank him or her for the careful reading and insightful suggestions. In the very first vers... | CAB | ACB | ABC | BCA | Selection 4 |
**A**:
Acknowledgements**B**: We are also very grateful to Davoud Cheraghi for pointing out a gap in an earlier version of the paper and providing many invaluable comments and suggestions. The second author was indebted to Institut de Mathématiques de Toulouse for its hospitality during his visit in 2014/2015 where an... | ACB | CBA | CAB | BAC | Selection 1 |
**A**: In Section 3 we prove the local index theorem for families of ∂¯¯\bar{\partial}over¯ start_ARG ∂ end_ARG-operators on Riemann orbisurfaces that are factors of the hyperbolic plane by the action of finitely generated cofinite Fuchsian groups. Specifically,**B**:
The paper is organized as follows**C**: Section 2 ... | ACB | ABC | CAB | BAC | Selection 3 |
**A**: Indeed, a special class of coupled SUSYs may be realized as harmonic oscillator-like systems, i.e. they satisfy the same Lie algebra and by virtue of Stone-von Neumann, may be realized in some way as harmonic oscillators. If one takes γ=−δ𝛾𝛿\gamma=-\deltaitalic_γ = - italic_δ, then the coupled SUSY equations b... | CAB | BCA | ACB | ABC | Selection 1 |
**A**: Within a row, tiles are unordered**B**: For counting purposes, we view them as ‘balls’ placed arbitrarily into ‘boxes’ labelled with the available markings**C**: The binomial coefficient (14) accounts for the remaining factors in the formula. The factors involving l𝑙litalic_l and n𝑛nitalic_n reduce to 1111 if ... | BAC | CBA | ABC | BAC | Selection 3 |
**A**: The first syzygy of Hibi rings is discussed in Section 3. Explicit expression for the first Betti number for planar distributive lattices has been discussed in Section 4.
**B**: In Section 2, we collect basic notations, terminology, and results that will be used in the paper**C**: The paper is structured as foll... | CBA | ABC | BCA | BAC | Selection 1 |
**A**: This is done by first calculating the dp-rank of a certain 1-based reduct of the group, and then studying the effect of re-introducing the order into that structure.
**B**: Theorem 1 is proved in Section 4**C**: The proof proceeds by showing that strongly dependent ordered abelian groups have finite spines and e... | ACB | ACB | CAB | ABC | Selection 3 |
**A**: To this end, one constructs from an atlas a proper étale Lie groupoids (see [MM03, Proposition 5.29])**B**: Recall from [Poh17, MM03] that every paracompact, smooth and effective orbifold can be represented by a so called atlas groupoid**C**: Following this procedure for a locally finite orbifold atlas, one sees... | BAC | ABC | BCA | CBA | Selection 1 |
**A**: The assumption made by Zeidler that the action of the group is free leads to the simplification that the controlled Hilbert space obtained from the L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-sections of the bundle on which the Dirac operator acts is already ample**B**: For proper a... | ABC | CBA | BCA | BAC | Selection 1 |
**A**: We remark that in this case, our method is similar to that of [MR3591945], with some differences. First we consider that T~~𝑇\tilde{T}over~ start_ARG italic_T end_ARG can be nonzero**B**: Also, our scheme is defined by a sequence of elliptic problems, avoiding the annoyance of saddle point systems. We had to re... | BAC | BCA | BAC | CBA | Selection 2 |
**A**: Now if T′superscript𝑇′T^{\prime}italic_T start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT is another element**B**: A∈I(M)𝐴𝐼𝑀A\in I(M)italic_A ∈ italic_I ( italic_M ) if
and only if FT(A⋇A)=0subscript𝐹𝑇superscript𝐴⋇𝐴0F_{T}(A^{\divideontimes}A)=0italic_F start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT ( itali... | CBA | CAB | BCA | BCA | Selection 1 |
**A**: I would also like to thank the anonymous referees for their many corrections and suggestions**B**: In particular for a suggested simplification of the proof of Lemma 4.2.**C**:
I would like to thank Mohammed Abouzaid, Marcel Bökstedt, Sylvain Courte, Tobias Ekholm, Yasha Eliashberg, Søren Galatius, and John Rog... | BCA | ACB | ABC | ACB | Selection 1 |
**A**:
Acknowledgement: The author would like thank Michael Finkelberg and Tatsuyuki Hikita for discussions, David Anderson and Hiroshi Iritani for helpful correspondences, and Thomas Lam for pointing out inaccuracies in a previous version of this paper**B**: This research was supported in part by JSPS KAKENHI Grant N... | ABC | ACB | BAC | BCA | Selection 2 |
**A**:
In general, the left- and right-cohomological dimensions of a monoid are not equal**B**: One immediate corollary of the above result is that if M𝑀Mitalic_M is a finitely presented special monoid with left- and right-cohomological dimensions both at least equal to 2222, then the left cohomological dimension of ... | ACB | CAB | BCA | BAC | Selection 1 |
**A**:
Recently, many external factors including changes in international situations, increase of war risk and significant environmental changes, all cause the financial market becomes much more volatile than before, and the financial market also has different orders of risk data mixed over a short period of time**B**... | ABC | BCA | BCA | BCA | Selection 1 |
**A**: This section is preparatory for Section 7.**B**:
In Section 6, we prove the independence of parameters for integrable highest weight representations of twisted affine Kac-Moody algebras over a base**C**: We also prove that the Sugawara operators acting on the integrable highest weight representations of twisted... | BAC | CAB | CBA | CBA | Selection 2 |
**A**: This statistical weight is clearly a special case of Eq**B**: (8) when there is only one type of real anyons, one type of boundaries, the number of boundaries is one, and only one pseudo-species. Hence, in light of Eqs. (2)-(5), the second binomial, i.e., the reduced statistical weight, in the statistical weight... | CBA | CBA | BCA | ACB | Selection 3 |
**A**:
IB and JPdS wish to thank the “Laboratoire International Associé” and the “Indo-French Program for Mathematics” of the CNRS as well as the International Research Staff Exchange Scheme “MODULI”, projet 612534 from the Marie Curie Actions of the European commission**B**: Finally, we are grateful for the referee’s... | ABC | BCA | ACB | CAB | Selection 3 |
**A**: In that case the conclusion follows easily from the induction hypothesis and the fact that for every α<β𝛼𝛽\alpha<\betaitalic_α < italic_β,**B**: We only need to argue for the conclusion in the case that β𝛽\betaitalic_β is a nonzero limit ordinal**C**:
The proof is by induction on β𝛽\betaitalic_β | ACB | CBA | CAB | BAC | Selection 2 |
**A**: We thank the referees for the careful reading of the first version of the text and for many helpful remarks**B**: This research was carried out within the HSE University Basic Research Program and funded by the Russian Academic Excellence Project ’5-100’**C**: The results of Section 4 has been obtained under sup... | ABC | CAB | ACB | BAC | Selection 1 |
**A**:
Any tubing of S𝑆Sitalic_S is isotopic to a tubing where each tube has one foot on the component of S𝑆Sitalic_S containing K𝐾Kitalic_K, and one foot on a closed component of S𝑆Sitalic_S**B**: In particular, it suffices to change tubes one at a time.**C**: Since tubes are boundaries of 3-dimensional 1-handles... | ACB | BAC | BAC | CAB | Selection 1 |
**A**: I would like to thank Christopher Dodd, Michael Groechenig and Tamas Hausel for helpful conversations**B**: I would like to thank Tsao-Hsien Chen and Siqing Zhang for useful comments on an earlier version of this paper.
**C**: I would like to thank my advisor Tom Nevins for many helpful discussions on this subje... | CBA | ABC | BCA | CAB | Selection 3 |
**A**: The proofs of Propositions**B**: We will prove them in a certain order to arrive at Corollaries 25 and 37, thus concluding by the optimality of the weight and the interpretation in terms of dual nonlinear semigroup**C**:
This section is devoted to the proofs of the results of Section 3 | BAC | CAB | BAC | CBA | Selection 4 |
**A**: This section is similar to that in [8]**B**: The differences focus on the quantitative hypothesis on the phase function which is introduced in [2] and will play
a crucial role in the induction argument via multilinear oscillatory estimates of Bennett, Carbery and Tao [3]. In particular, we emphasize the role pla... | ABC | BCA | CBA | CBA | Selection 2 |
**A**: To be precise, we are interested in the following stochastic nonlinear wave equation on a smooth bounded domain 𝒪⊂ℝ2𝒪superscriptℝ2{\mathscr{O}}\subset\mathbb{R}^{2}script_O ⊂ blackboard_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT,**B**:
Our aim here is to extend the existing studies to the wave equation wit... | CBA | BCA | CAB | BCA | Selection 3 |
**A**:
In characteristic zero, symplectic cohomology SHSH{\operatorname{SH}}roman_SH is known to have the structure of a BV-algebra (see e.g**B**: the BV operator is compatible with a product and a bracket, both given by counting pairs of pants but with asymptotic markers treated differently.**C**: [1]), i.e | ACB | CBA | CBA | BAC | Selection 1 |
**A**:
We close this paper with the consideration that we used the notion of up-adjacency to define our Markov chain**B**: One may define a similar process using the notion of down-adjacency**C**: But it is not trivial to relate this new walk to the spectrum of the Laplacian. If it can be done, one is one step closer ... | BCA | BCA | CAB | ABC | Selection 4 |
**A**: Those**B**: point ⟨X⟩delimited-⟨⟩𝑋\langle X\rangle⟨ italic_X ⟩ determines the 17171717-space 𝕁17cABsuperscriptsubscript𝕁17𝑐𝐴𝐵\mathbb{J}_{17}^{cAB}blackboard_J start_POSTSUBSCRIPT 17 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_c italic_A italic_B end_POSTSUPERSCRIPT**C**: We also note that
X𝑋Xitalic_X... | BCA | CAB | BCA | CBA | Selection 2 |
**A**:
This topology is referred to as the induced topology of δ𝛿\deltaitalic_δ**B**: It is always completely regular, and is Hausdorff if and only if the proximity δ𝛿\deltaitalic_δ is separated**C**: Every separated proximity space admits a unique (up to a proximity isomorphism) compactification, which we describe ... | ABC | ACB | BAC | BAC | Selection 1 |
**A**: italic_g **B**: , C¯¯=A¯¯∗B¯¯¯¯𝐶¯¯𝐴¯¯𝐵\overline{\overline{C}}=\overline{\overline{A}}\,*\,\overline{\overline{B}}over¯ start_ARG over¯ start_ARG italic_C end_ARG end_ARG = over¯ start_ARG over¯ start_ARG italic_A end_ARG end_ARG ∗ over¯ start_ARG over¯ start_ARG italic_B end_ARG end_ARG)
implies regular matri... | BCA | CAB | BAC | ACB | Selection 1 |
**A**: Both type 2 and type 3 (whose precise descriptions are given below) are log smooth extensions of rational type**B**: In type 2, the residue extension is of transcendence degree 1 and the extension of the value group is finite**C**: In type 3, the residue extension is trivial.
| CBA | ABC | CBA | ACB | Selection 2 |
**A**: a𝑎aitalic_a if p=apc𝑝𝑎subscript𝑝𝑐p=ap_{c}italic_p = italic_a italic_p start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT**B**: The**C**: By contrast, we conjecture that pcsubscript𝑝𝑐p_{c}italic_p start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is sharp in
Conjecture 6.3 | CBA | BAC | ACB | CAB | Selection 3 |
**A**: 2.8] for log canonical pairs (for a smooth complex projective variety X𝑋Xitalic_X).**B**: 4.2] and [D15, Thm**C**:
Using Theorem 6.2, we establish a precise comparison between two L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT extension theorems of [K10, Thm | ACB | ABC | ACB | CBA | Selection 4 |
**A**: This is because the randomized data is not localized and has the same amplitude at each point of the domain. In comparison, the deterministic scaling threshold does not depend on the geometry because it corresponds to the data zoomed out at a point, which is localized.**B**: For compact manifold the canonical ra... | ACB | CAB | CBA | CAB | Selection 3 |
**A**: The fine structure to a large extent revolves around understanding the leaves of classifying trees**B**: The leaves are controlled by depth zero types and so we remind the reader of the definition (for more definitions and classical results consult the Appendix).**C**:
Since the proof of the structure theorem, ... | ACB | ACB | BCA | CAB | Selection 3 |
**A**: the inclusion need not be full.**B**:
As 𝒜𝒜\mathcal{A}caligraphic_A is semi-simple, any tensor functor on 𝒜𝒜\mathcal{A}caligraphic_A is automatically faithful**C**: We are not asking that 𝒜𝒜\mathcal{A}caligraphic_A is embedded in 𝒞𝒞\mathcal{C}caligraphic_C, ie | BCA | CAB | ABC | ACB | Selection 2 |
**A**: The geometry of Kazhdan-Lusztig varieties in (Kac–Moody) flag varieties is also closely related to formulas that compute the restriction of torus-equivariant
cohomology/K𝐾Kitalic_K-theoretic Schubert classes to fixed points**B**: Since Kazhdan-Lusztig varieties degenerate to subword complexes, their Hilbert ser... | ACB | ABC | BCA | CAB | Selection 2 |
**A**: As we can see from the description so far, there is a heavy emphasis on the the fact that all of our objects are framed**B**: Without the framing, we would need to take the Stokes data up to conjugation by diagonal matrices to get something well defined on isomorphism classes. We should also remark that the idea... | ACB | CBA | BCA | BCA | Selection 1 |
**A**: We refer to the introduction of the latter article for further**B**: Some models in financial mathematics and econometrics are threshold diffusions, for instance continuous-time versions of SETAR (self-exciting threshold auto-regressive) models, see e.g. [15, 41]**C**: SBM and OBM and their local time have been ... | ABC | ACB | BAC | CAB | Selection 4 |
**A**: However, such computational efficiency guarantees rely on the regularity condition that the state space is already well explored**B**: Such a condition is often implied by assuming either the access to a “simulator” (also known as the generative model) (Koenig and Simmons, 1993; Azar et al., 2011, 2012a, 2012b; ... | BCA | CBA | ABC | CBA | Selection 1 |
**A**: The first three authors would also like to thank Eric Stucky for his edits to this paper and Amal Mattoo for his contributions to this research.
The fourth author was supported by the Trond Mohn Foundation project “Algebraic and Topological Cycles in Complex and Tropical Geometries”.**B**: The first three author... | CBA | ACB | BCA | ABC | Selection 1 |
**A**: The Erdós-Straus conjecture can also be rephrased as a problem of an inequality. That is to say, the conjecture can be restated as saying that for all n≥3𝑛3n\geq 3italic_n ≥ 3 the inequality holds**B**:
Despite its apparent simplicity, the problem still remain unresolved. However there has been some noteworthy... | BCA | CAB | BAC | ACB | Selection 2 |
**A**: Many of the remaining did not have a convex partition supporting the choice of line bundles. The next example is an example of this; in this case (but not usually), one is able to find a degeneration of the complete intersection to a toric variety; we find the Laurent polynomial associated to this toric variety ... | ABC | BAC | CAB | ABC | Selection 3 |
**A**: Recently in [39], the second author and J.J. Xu got the boundary gradient estimates and the corresponding existence theorem for the Neumann boundary value problem on mean curvature equation.
**B**: Also, we recommend the recent book written by Lieberman [33] for the Neumann and the oblique derivative problems of... | ACB | BCA | CBA | ABC | Selection 3 |
**A**: The Fourier transform of this function when t=1𝑡1t=1italic_t = 1 is**B**: We will employ as bump functions t∇hPt𝑡subscript∇ℎsubscript𝑃𝑡t\nabla_{h}P_{t}italic_t ∇ start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_P start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT, where ∇hPtsubscript∇ℎsubscript𝑃𝑡\nabla_{... | CAB | ABC | CBA | ABC | Selection 3 |
**A**: The following statement regarding products of filtrations are obtained at the simplicial level (and in more generality) in [72, Proposition 2.6] and in [42, 73]**B**: These proofs operate at the simplicial level.**C**: The statement about metric gluings appeared in
[7, Proposition 4] and [68, Proposition 4.4] | ACB | CAB | ABC | CAB | Selection 1 |
**A**: A more difficult task would be to consider other types of regularity regimes, e.g**B**: the fractional Sobolev one. For this direction, See [44] and the discussions therein.**C**:
Based on the observations made in this article, the proofs of [14, 15] for the rigidity statements are also valid under little Hölde... | ACB | BCA | ACB | BAC | Selection 2 |
**A**: Therefore
x∈ϕ−1(ϕ(φσ−1(ψτ→−1(x))))𝑥superscriptitalic-ϕ1italic-ϕsuperscriptsubscript𝜑𝜎1superscriptsubscript𝜓→𝜏1𝑥x\in\phi^{-1}(\phi(\varphi_{\sigma}^{-1}(\psi_{\overrightarrow{\tau}}^{-1}(x))))italic_x ∈ italic_ϕ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( italic_ϕ ( italic_φ start_POSTSUBSCRIPT ital... | CBA | BCA | ACB | CBA | Selection 2 |
**A**: We do not know, but this question can be seen as a test for the condensed wall gadget**B**: If it is proven that ladders with 13 rungs still do not possess the edge-Erdős-Pósa property, then clearly there is a counterexample graph not based on a condensed wall**C**: However, if it is shown that ladders with 13 r... | CBA | CAB | ACB | ABC | Selection 4 |
**A**: As a result the expression under square**B**: Indeed, we have bS=−5subscript𝑏𝑆5b_{S}=-5italic_b start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT = - 5, bI=4subscript𝑏𝐼4b_{I}=4italic_b start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT = 4 and
D=bS2−bI2=(3)2𝐷superscriptsubscript𝑏𝑆2superscriptsubscript𝑏𝐼2supers... | CBA | CAB | CAB | BCA | Selection 1 |
**A**: One popular approach is to employ verification arguments to check if a given solution of the HJB equation coincides with the value function at hand, and obtain as a byproduct the optimal control**B**: In the Markovian case, a classical approach in solving stochastic control problems is given by the dynamic progr... | BAC | CAB | CBA | ABC | Selection 1 |
**A**: The construction used to prove Theorem 6 can also be used to obtain results which are not immediate corollaries of the theorem (or its corollary for automaton semigroups in 8)**B**: The version for automaton semigroups does not follow directly from 8, as the free monogenic semigroup is not a complete automaton s... | BCA | CBA | ACB | BCA | Selection 3 |
**A**: Introducing a refined variant of the Euler totient function tailored to specific subsets of real numbers, characterized by right continuity while upholding the essence of the original function, paves a seamless path beyond this anticipated obstacle.**B**: The inherent limitation of the Euler totient function, re... | CBA | BCA | ACB | ACB | Selection 1 |
**A**: K.C. was supported by the KIAS Individual Grant MG078902, a POSCO Science Fellowship, an Asian Young Scientist Fellowship, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2023-00219980). C.M. was supported by the NSF grant DMS-1905165**B**: F.S. was supported b... | CAB | ACB | BCA | CBA | Selection 3 |
**A**: Then, it will remain to observe that combinatorially relevant terms cancel and that the remaining terms can be bounded sufficiently well, uniformly in m𝑚mitalic_m. This proof is quite lengthy. Indeed, expanding the square will lead to terms with up to 5555 indices, thus giving rise to a huge number of cases tha... | CAB | BAC | CBA | BCA | Selection 1 |
**A**: Staller, d𝑑ditalic_d means the vertex is already claimed by Dominator**B**: And n𝑛nitalic_n refers to “null” which means that the vertex
is still free — not yet claimed by any player in the current game**C**: While 1111 means that the vertex is already dominated, | BCA | ACB | ABC | ACB | Selection 3 |
**A**: Then in Section 4 we establish the tropical/holomorphic correspondence for Maslov index zero discs with boundary on special Lagrangian fibres. Then we prove the equivalence of counting of Maslov index two discs with the same boundary conditions with the weighted count of broken lines in Section 5. This includes ... | CAB | CBA | BAC | BCA | Selection 1 |
**A**: The family (6.1) is of type 2+ 2+ 2 whenever the parameter t𝑡titalic_t is a root of unity**B**: Its feature is the presence of a right angle; in fact the spaces of this family all belong to the self-conjugated spaces studied in Section 4.1**C**: Up to homothety they form a family parametrized by a rational num... | BCA | ACB | CAB | ABC | Selection 4 |
**A**: One choice of the groups that can provide nontrivial twist as well as good physical meaning is the loop groups LG𝐿𝐺LGitalic_L italic_G with G𝐺Gitalic_G a compact Lie group.
**B**: The problem does not lie in what the elliptic cohomology theory is, but the property of the equivariant groups directly**C**: One... | ABC | CBA | BCA | CAB | Selection 2 |
**A**: This will be bootstrapped to the multi-color case in later sections**B**: We**C**: Note that the 1111-color case with the completeness requirement is not very interesting, and also not useful for the general case: completeness states that every node on
the left must be connected, via the unique edge relation, to... | ABC | CBA | ACB | BCA | Selection 3 |
**A**: For instance, there is a version of 2222-henselian valuations for fields with non-trivial radicals [9], useful in Galois Theory (see Example 23)**B**: The next problem follows the same idea.**C**:
Cordes also found that many results concerning quadratic forms and related subjects are still valid when replacing ... | BAC | BCA | ABC | CAB | Selection 2 |
**A**: Szepesvári, 2018; Dalal et al., 2018; Srikant and Ying, 2019) settings. See Dann et al. (2014) for a detailed survey. Also, when the value function approximator is linear, Melo et al. (2008); Zou et al**B**: (2019); Chen et al. (2019b) study the convergence of Q-learning. When the value function approximator is ... | BAC | ABC | CAB | ACB | Selection 2 |
**A**: In particular, we would want to rigidify homotopy coherent comultiplications and coactions.
However, we face multiple obstacles**B**: As in algebras, we need to construct homotopy coherent coalgebraic structures**C**: Firstly, a common assumption for algebras and modules is that the monoidal product is closed an... | ACB | ABC | BAC | BCA | Selection 3 |
**A**: }\end{cases}italic_v ( italic_x ) ≔ { start_ROW start_CELL roman_min start_POSTSUBSCRIPT italic_y ∈ italic_I start_POSTSUBSCRIPT italic_π , italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT italic_f ( italic_y ) end_CELL start_CELL if italic_x ∈ blackboard_T start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT start_POSTSU... | ABC | BCA | ABC | CAB | Selection 2 |
**A**: We turn to non-zero weak sequential limit points**B**: First of all, for very special spaces, the existence of a non-zero weak sequential limit point does imply hypercyclicity**C**: Recall that a Banach space has the Schur property if every weakly convergent sequence converges; and a Fréchet space is a Montel sp... | ACB | ABC | CAB | BCA | Selection 2 |
**A**:
Many aspects of 2222-category theory benefit from a passage to double categories**B**: For example, a good notion of limit for 2222-categories is that of a 2222-limit, where the universal property is expressed by an isomorphism between hom-categories, rather than hom-sets**C**: As clingman and the author show i... | BAC | ABC | CAB | CAB | Selection 2 |
**A**: However, we will denote**B**: Strictly speaking, the above definitions apply only to the case where GG\rm Groman_G is special**C**: When GG\rm Groman_G is not special, the above objects will in fact need to be replaced by the derived push-forward of the above objects viewed as sheaves on the
big étale site of ... | BCA | CBA | BAC | CAB | Selection 4 |
**A**: These were introduced in joint work with Sven Meinhardt in [DM20], as part of a project to realise the cohomological Hall algebras defined by Kontsevich and Soibelman [KS11] as positive halves of generalised Yangians**B**: The construction of the BPS Lie algebra for arbitrary symmetric quivers with potential is ... | CBA | ABC | BAC | ACB | Selection 3 |
**A**: It is motivated by Steiner’s formula relating curvatures to the change in area under parallel surfaces**B**: The main result is to prove the correspondence between discrete CMC-1 surfaces and circle patterns (Theorem 0.2).**C**:
In this section, we define a notion of integrated mean curvature on horospherical n... | BCA | ACB | CBA | BAC | Selection 1 |
**A**: exists a finite set F⊆V1𝐹subscript𝑉1F\subseteq V_{1}italic_F ⊆ italic_V start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT such that ∀x∈V1,∃x′∈F,x≡1x′formulae-sequencefor-all𝑥subscript𝑉1formulae-sequencesuperscript𝑥′𝐹subscript1𝑥superscript𝑥′\forall x\in V_{1},\exists x^{\prime}\in F,x\equiv_{1}x^{\prime}∀ italic_x ... | ABC | BAC | CAB | CBA | Selection 1 |
**A**: Figure 2 illustrates both diagrams combined, along with all the ZFC-provable inequalities that we are aware of**B**: See [Bla10, BJ95] for the definitions and the proofs for the inequalities (with the exception of cof(ℳ)≤𝔦cofℳ𝔦{\operatorname{cof}(\mathcal{M})}\leq\mathfrak{i}roman_cof ( caligraphic_M ) ≤ frak... | BCA | CBA | CBA | CBA | Selection 1 |
**A**: One of them is called a parabolic visual metric based on the vertical geodesic in some negatively curved solvable Lie groups in [24]**B**: It should be noted that this parabolic visual metric was formerly named Euclid–Cygan metric by Hersonsky and Paulin [20] in the study of the rigidity of discrete isometry gro... | CBA | CAB | ACB | CAB | Selection 3 |
**A**: The reader is referred to [MJT21a, § 3] and [BG21, § 11] for examples of spherical homogeneous spaces for which versions of Proposition 1.1 and Theorem 1.3 are applied to determine their (k,F)𝑘𝐹(k,F)( italic_k , italic_F )-forms**B**: Other results, based in part on a weaker version of Proposition 1.1, concern... | ACB | BCA | ACB | ACB | Selection 2 |
**A**:
A natural generalisation of the above processes are the broad family of Markov Additive Processes (MAPs), which incorporate an externally influencing Markov environment, providing greater flexibility to the characteristics of the underlying process in terms of its claim frequency and severity distributions, see... | ABC | ACB | BCA | ABC | Selection 2 |
**A**: It has been shown that in some circumstances, faster dispersal is sometimes selected for [46, 49]. See also [27, 40, 48]. We also mention the work [36] on the evolution of dispersal in phytoplankton populations, where individuals compete non-locally for sunlight.
**B**: We mention the work of [30, 34, 42, 45] fo... | BCA | CBA | ACB | BAC | Selection 2 |
**A**: The chain with respect to which one is considering representation stability there is of course still the chain of symmetric groups. Thus, representation stability with respect to a chain of diagrammatically defined algebras is not considered in [1] (Barter, Entova-Aizenbud, Heidersdorf).**B**: Diagrammatically d... | CAB | BCA | CBA | ACB | Selection 3 |
**A**: The 3-regular Cayley graph can be transformed to a 4-regular graph middle pages graph (Fig.8) that offers each branching number an Eulerian tour, in line with classic 3-to-4-regular transformations**B**: René Descartes (1596-1650) knew that packaging an infinite number of cubes with three edges at each node give... | ACB | BAC | CBA | ABC | Selection 1 |
**A**: Moreover, multiplying the product above by the left-hand side of Theorem 1.4 yields the octuple product in 4.13**B**: Hence under Theorem 1.4, the octuple identity and Proposition 5.4 are equivalent.
**C**: The q𝑞qitalic_q-coefficients in the right-hand side above are the same (up to a sign) as the q𝑞qitalic_q... | CBA | CBA | CAB | BCA | Selection 4 |
**A**: One of the main difficulties in proving a contraction theorem in the Kähler category is the lack of a base-point free theorem analogous to that of [KM98, Theorem 3.3] in the projective case**B**: However, there is a base-point free conjecture in the Kähler category involving nef and big cohomology classes which ... | ACB | ABC | BCA | BAC | Selection 1 |
**A**: Surprisingly, this is sharper than both our estimate in Corollary 3 and Sarnak and Xue’s estimate (but still weaker than Marshall’s estimate) for the compact case**B**: In the real hyperbolic case, our estimates extend Yeung’s estimates for cocompact lattices [Yeu94, Theorem 2.4.1] to noncocompact lattices.
**C*... | BCA | CBA | ACB | BAC | Selection 3 |
**A**: More specifically, we proved**B**:
In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\}^{n}{ - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT which have modulus 1111 fails**C**... | ACB | ABC | CAB | ACB | Selection 3 |
**A**: This Dyson process of mutually avoiding Brownian motions is a leading player [OY02] in**B**:
The OU dynamics on GUE induces a form of Dyson’s Brownian motion [Dys62] on the eigenvalues**C**: In fact this can be used to also prove the value of the highest eigenvalue starts de-correlating at the same time scale o... | BAC | CAB | CBA | BAC | Selection 2 |
**A**:
In the original definition of separation profile, the subset which is removed is a subset of vertices**B**: But for bounded degree graphs, it is easy to see that the two resulting definitions of separation profiles have same asymptotic behaviors**C**: Moreover, the advantage of working with edges instead of ver... | ACB | BAC | ABC | BCA | Selection 3 |
**A**: However, Floater-Hormann becomes indistinguishable from 5thsuperscript5𝑡ℎ5^{th}5 start_POSTSUPERSCRIPT italic_t italic_h end_POSTSUPERSCRIPT-order splines.
Further, when considering the amount of coefficients/nodes required to determine the interpolant, plotted in the right panel (with logarithmic scales on bo... | ACB | BCA | CAB | ACB | Selection 2 |
**A**:
In the remaining part of this section we shall prove Theorems 1.1 and 1.2 at one stroke**B**: Nevertheless, in this case we need to pay extra care to fix a cohomology class.**C**: The proof of Theorem 1.1 essentially follows from (and is somewhat simpler than) that of its local variant, i.e., Theorem 1.2, as we... | BCA | ACB | CAB | ABC | Selection 2 |
**A**: Conditions for such families of maps to define a permutation of the field 𝔽𝔽\mathbb{F}blackboard_F are well studied and established for special classes like Dickson polynomials [20], linearized polynomials [21] and few other specific forms [13, 14] to name a few.
**B**: Some well-studied families of polynomial... | BAC | BCA | CBA | BAC | Selection 3 |
**A**: Now every Rauzy class may contain both untwisted and twisted IRE schemes, however the twist total value is the same for the whole class. Induction can transfer turns between a scheme and its dual, while the twist total remains unchanged.
**B**: The last proposition adds one more argument towards the necessity of... | ABC | BAC | BAC | CAB | Selection 4 |
**A**: Then we define the local minima of such problems, followed by the assumptions we use in our convergence**B**: We start with the definition
of the key geometry property of sets involving sparse and low-rank optimization problems**C**: This section is organized as follows | CAB | BCA | ACB | CBA | Selection 4 |
**A**: This type of weak dissipative structure has been recently observed for several interesting systems, e.g. the Timoshenko system with the Fourier law [23] or the Cattaneo law [24] of heat conductions.**B**:
which exactly coincides with the one in [35, Theorem 1.2]**C**: The estimate (3.21) shows the strict dissip... | BCA | CBA | CAB | BCA | Selection 3 |
**A**: We consider it interesting to discuss the direct and inverse problems in general. In fact, one may expect that solutions of these questions would yield classification results similar to the one of [BGT12].**B**: Indeed, it can be restated to say that Lie cores of piecewise definable subgroups generated by pseudo... | BAC | ACB | BAC | CBA | Selection 4 |
**A**: Not every FAOM is realizable as ℒ(𝒜)ℒ𝒜\mathscr{L}(\mathscr{A})script_L ( script_A ) for a finitary arrangement**B**:
Our “Finitary Affine Oriented Matroids” axiomatize properties of the polyhedral stratification of Euclidean space induced by finitary hyperplane arrangements**C**: Still, some familiar geometr... | ABC | CAB | BAC | ABC | Selection 3 |
**A**: To fix this, we will show that (28) is actually induced by a pullback map.**B**: However, this argument does not prove that (28) is an isomorphism of rings, not just of A∗(pt)superscript𝐴ptA^{*}(\mathrm{pt})italic_A start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( roman_pt )-modules**C**:
obtained in [DoZh], see... | CAB | CAB | BCA | CBA | Selection 4 |
**A**: This technique formulates the objective function and constraints using linear matrix inequalities (LMIs) to synthesize a Markov chain capable of achieving a desired distribution while adhering to specified transition constraints. Notably, this study does not impose any assumptions on the Markov chain, rendering ... | CAB | BAC | BCA | CBA | Selection 1 |
**A**: §2.1). Consequently, many of the obstructions involved in Corollary 1.17 follow simply from singular homology considerations (c.f. Remark 6.4).**B**:
We note, however, that Weinstein embeddings have more restricted topology compared to Liouville embeddings**C**: Namely, the complementary cobordism must admit a ... | CBA | CAB | BCA | ACB | Selection 2 |
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