Extension of Bernstein Polynomials to Infinite Dimensional Case

The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting. The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space.Comment: 14 pages. to appear on Journal of Approximation Theor

Entire solutions of certain fourth order elliptic problems and related inequalities

We study distributional solutions of semilinear biharmonic equations of the type Δ2u+f(u)=0 onℝN, where f is a continuous function satisfying f (t)t ≥ c |t|q+1 for all t ∈ ℝ with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy- Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions

A new critical curve for a class of quasilinear elliptic systems

We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given by the $p$-Laplacian operator as well as the mean curvature operator in non parametric form. We prove that if the exponents lie under a certain curve, then the system has only the trivial solution. These results hold without any restriction provided the possible solutions are more regular. The underlying framework is the classical Euclidean case as well as the Carnot groups setting.Comment: 28 page

Targeting cyclin-dependent kinases in sarcoma treatment: Current perspectives and future directions

Effective treatment of advanced/metastatic bone and soft tissue sarcomas still represents an unmet medical need. Recent advances in targeted therapies have highlighted the potential of cyclin-dependent kinases (CDK) inhibitors in several cancer types, including sarcomas. CDKs are master regulators of the cell cycle; their dysregulation is listed among the “hallmarks of cancer” and sarcomas are no exception to the rule. In this review, we report both the molecular basis, and the potential therapeutic implications for the use of CDK inhibitors in sarcoma treatment. What is more, we describe and discuss the possibility and biological rationale for combination therapies with conventional treatments, target therapy and immunotherapy, highlighting potential avenues for future research to integrate CDK inhibition in sarcoma treatment

Tunable Two-Photon Quantum Interference of Structured Light

Structured photons are nowadays an important resource in classical and quantum optics due to the richness of properties they show under propagation, focusing, and in their interaction with matter. Vectorial modes of light in particular, a class of modes where the polarization varies across the beam profile, have already been used in several areas ranging from microscopy to quantum information. One of the key ingredients needed to exploit the full potential of complex light in the quantum domain is the control of quantum interference, a crucial resource in fields like quantum communication, sensing, and metrology. Here we report a tunable Hong-Ou-Mandel interference between vectorial modes of light. We demonstrate how a properly designed spin-orbit device can be used to control quantum interference between vectorial modes of light by simply adjusting the device parameters and no need of interferometric setups. We believe our result can find applications in fundamental research and quantum technologies based on structured light by providing a new tool to control quantum interference in a compact, efficient, and robust way

Resilience of hybrid optical angular momentum qubits to turbulence

Recent schemes to encode quantum information into the total angular momentum of light, defining rotation-invariant hybrid qubits composed of the polarization and orbital angular momentum degrees of freedom, present interesting applications for quantum information technology. However, there remains the question as to how detrimental effects such as random spatial perturbations affect these encodings. Here, we demonstrate that alignment-free quantum communication through a turbulent channel based on hybrid qubits can be achieved with unit transmission fidelity. In our experiment, alignment-free qubits are produced with q-plates and sent through a homemade turbulence chamber. The decoding procedure, also realized with q-plates, relies on both degrees of freedom and renders an intrinsic error-filtering mechanism that maps errors into losses

Deterministic qubit transfer between orbital and spin angular momentum of single photons

In this work we experimentally implement a deterministic transfer of a generic qubit initially encoded in the orbital angular momentum of a single photon to its polarization. Such transfer of quantum information, completely reversible, has been implemented adopting a electrically tunable q-plate device and a Sagnac interferomenter with a Dove's prism. The adopted scheme exhibits a high fidelity and low losses.Comment: 3 pages, 2 figure

Universal Constraints on Low-Energy Flavour Models

It is pointed out that in a general class of flavour models one can identify certain universally present FCNC operators, induced by the exchange of heavy flavour messengers. Their coefficients depend on the rotation angles that connect flavour and fermion mass basis. The lower bounds on the messenger scale are derived using updated experimental constraints on the FCNC operators. The obtained bounds are different for different operators and in addition they depend on the chosen set of rotations. Given the sensitivity expected in the forthcoming experiments, the present analysis suggests interesting room for discovering new physics. As the highlights emerge the leptonic processes, $\mu\rightarrow e\gamma$, $\mu\rightarrow eee$ and $\mu\rightarrow e$ conversion in nuclei.Comment: 18 pages, 3 figures; v2 matches published versio

The Messenger Sector of SUSY Flavour Models and Radiative Breaking of Flavour Universality

The flavour messenger sectors and their impact on the soft SUSY breaking terms are investigated in SUSY flavour models. In the case when the flavour scale M is below the SUSY breaking mediation scale M_S, the universality of soft terms, even if assumed at M_S, is radiatively broken. We estimate this effect in a broad class of models. In the CKM basis that effect gives flavour off-diagonal soft masses comparable to the tree-level estimate based on the flavour symmetry.Comment: 24 pages, 3 figures. v3: minor changes in the text, typos corrected, version accepted for publication in JHE