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Exactly solvable mirror pairs of Calabi–Yau threefolds of hypersurface type exist in the class of Gepner models that include nondiagonal affine invariants. Motivated by the string theoretic automorphy established previously for models in this class, it is natural to ask whether the arithmetic structure of mirror pairs varieties reflects the fact that as conformal field theories, they are isomorphic. Mirror symmetry in particular predicts that the L-functions of the Ω-motives of such pairs are identical. In this paper this prediction is confirmed by showing that the Ω-motives of exactly solvable mirror pairs are isomorphic. This follows as a corollary of the proof of a more general result establishing an isomorphism between nondiagonally and diagonally induced motives in this class of varieties. The motivic approach formulated here circumvents the difficulty that no mirror construction of the Hasse–Weil zeta function is known.

The aim of the study was to investigate the association between the performance in two clinical tests for the endurance of deep neck flexors [Craniocervical Flexion Test (CCFT) and Chin Tuck Neck Flexion Test (CTNFT)] and the motivation of participants to continue and complete physical activities. Twenty-one healthy volunteers participated (men/women 13/8, age 21.1$\pm$1.37 years). Participants were asked to complete the Assessment Scale for Completion of Usual Physical Activities (ASCUPA), the Short Scale of Physical Activity Motives (SSPAM), a visual analog scale for the recording of their motivation to complete a physical activity (VAS motivation) and then they performed the CCFT and CTNFT. The CCFT did not present any significant correlation with either VAS motivation or ASCUPA. The CTNFT was not significantly associated with VAS motivation, but it was significantly correlated with ASCUPA ($r_s=0.58$, $p<0.01$). Furthermore, the CTNFT was significantly correlated with the total number of motives for physical activity ($r_s=0.64$). The correlation between the performance of the two tests was not significant ($r_s=0.16$, $p>0.05$). The findings suggest that only the CTNFT is dependent on participants’ motivation to complete an activity.

We prove a number of basic vanishing results for modified diagonal classes. We also obtain some sharp results for modified diagonals of curves and abelian varieties, and we prove a conjecture of O’Grady about modified diagonals on double covers.

We investigate how the motive of hyper-Kähler varieties is controlled by weight-2 (or surface-like) motives via tensor operations. In the first part, we study the Voevodsky motive of singular moduli spaces of semistable sheaves on K3 and abelian surfaces as well as the Chow motive of their crepant resolutions, when they exist. We show that these motives are in the tensor subcategory generated by the motive of the surface, provided that a crepant resolution exists. This extends a recent result of Bülles to the O’Grady-10 situation. In the non-commutative setting, similar results are proved for the Chow motive of moduli spaces of (semi-)stable objects of the K3 category of a cubic fourfold. As a consequence, we provide abundant examples of hyper-Kähler varieties of O’Grady-10 deformation type satisfying the standard conjectures. In the second part, we study the André motive of projective hyper-Kähler varieties. We attach to any such variety its defect group, an algebraic group which acts on the cohomology and measures the difference between the full motive and its weight-2 part. When the second Betti number is not 3, we show that the defect group is a natural complement of the Mumford–Tate group inside the motivic Galois group, and that it is deformation invariant. We prove the triviality of this group for all known examples of projective hyper-Kähler varieties, so that in each case the full motive is controlled by its weight-2 part. As applications, we show that for any variety motivated by a product of known hyper-Kähler varieties, all Hodge and Tate classes are motivated, the motivated Mumford–Tate conjecture 7.3 holds, and the André motive is abelian. This last point completes a recent work of Soldatenkov and provides a different proof for some of his results.

The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First, we prove a Beauville–Voisin type theorem for zero-cycles on double EPW sextics; precisely, we show that the codimension-4 part of the subring of the Chow ring of a double EPW sextic generated by divisors, the Chern classes and codimension-2 cycles invariant under the anti-symplectic covering involution has rank one. Second, for double EPW sextics birational to the Hilbert square of a K3 surface, we show that the action of the anti-symplectic involution on the Chow group of zero-cycles commutes with the Fourier decomposition of Shen–Vial.

Differences between male and female entrepreneurs provide compelling reasons to study the latter separately. Especially in rural areas, research shows that women are a remarkable and unexplored source of the labor force. Nevertheless, few researchers have examined rural women and the issues pertaining to their entrepreneurship separately. The contribution of this study to the debate of women entrepreneurship is the closer examination of women in Greek rural areas. This research aims to examine factors that must be considered independently with recognition to the variances of rural areas with different geomorphologic and economic profiles. The characteristics of women entrepreneurship in Greek rural areas and the women's motives for the undertaking of the entrepreneurial activity are used to identify a typology of women entrepreneurs in the Greek countryside.

Let $X$ be a compact Riemann surface of genus $g\ge 2$ and let $D\subset X$ be a fixed finite subset. We considered the moduli spaces of parabolic Higgs bundles and of parabolic connections over $X$ with the parabolic structure over $D$. For generic weights, we showed that these two moduli spaces have equal Grothendieck motivic classes and their $E$-polynomials are the same. We also show that the Voevodsky and Chow motives of these two moduli spaces are also equal. We showed that the Grothendieck motivic classes and the $E$-polynomials of parabolic Higgs moduli and of parabolic Hodge moduli are closely related. Finally, we considered the moduli spaces with fixed determinants and showed that the above results also hold for the fixed determinant case.

In [A formulation of conjectures on p-adic zeta functions in non-commutative Iwasawa theory, in Proc. St. Petersburg Mathematical Society, Vol. 12, American Mathematical Society Translations, Series 2, Vol. 219 (American Mathematical Society, Providence, RI, 2006), pp. 1–85] Fukaya and Kato presented equivariant Tamagawa number conjectures that implied a very general (non-commutative) Iwasawa main conjecture for rather general motives. In this article we apply their methods to the case of one-parameter families of motives to derive a main conjecture for such families. On our way there we get some unconditional results on the variation of the (algebraic) λ- and μ-invariant. We focus on the results dealing with Selmer complexes instead of the more classical notion of Selmer groups. However, where possible we give the connection to the classical notions.

We study variations of Hodge structures over a Picard modular surface, and compute the weights and types of their degenerations through the cusps of the Baily–Borel compactification. These computations are one of the key inputs which allow Wildeshaus [On the interior motive of certain Shimura varieties: the case of Picard surfaces, Manuscripta Math.148(3) (2015) 351–377] to construct motives associated with Picard modular forms.

Polylogarithms are those multiple polylogarithms that factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic quotient. Building on work of Dan-Cohen, Wewers, and Brown, we push the computational boundary of our explicit motivic version of Kim’s method in the case of the thrice punctured line over an open subscheme of $\mathrm{\text{Spec }}\mathbb{Z}$. To do so, we develop a greatly refined version of the algorithm of Dan-Cohen tailored specifically to this case, and we focus attention on the polylogarithmic quotient. This allows us to restrict our calculus with motivic iterated integrals to the so-called depth-one part of the mixed Tate Galois group studied extensively by Goncharov. We also discover an interesting consequence of the symmetry-breaking nature of the polylog quotient that forces us to symmetrize our polylogarithmic version of Kim’s conjecture. In this first part of a two-part series, we focus on a specific example, which allows us to verify an interesting new case of Kim’s conjecture.

Low employability among specific populations (e.g. religious/traditional women, the elderly, disabled workers, and immigrants) has unfavourable consequences on the unemployed individual, society, and the state economy. The latter include poverty, a heavy toll on welfare budgets, diminished growth, and an increase in the ‘dependency ratio’. We suggest a rather novel policy (borrowed from the field of Vocational Psychology) that could lead to successful integration into the labour market of low-employability populations: The design of tailor-made training programmes that respond to work motives, coupled with a working environment that caters to special needs/restrictions, and complemented with counselling and monitoring. The suggested strategy is illustrated using a case study of Israeli ultra-Orthodox women, who exhibit lower employment rates than other Israeli women. The motives behind their occupational choices are explored based on data collected by a survey. Factor Analysis is employed to sort out the motives behind their occupational choices, and regression analysis is used to associate job satisfaction with work motivation. Policy implications are suggested based on the findings. There is already some evidence on the successful outcomes of the proposed strategy.