The sampling theorem of Whittaker (1915) [31], Kotelnikov (1933) [25] and Shannon (1949) [28] gives cardinal series representations for finite L2-Fourier transforms at equidistant sampling points. Here we investigate the situation when the Fourier transform is replaced by a perturbed one. Thus the kernel of the transform will be of the form exp(−ixt)+ε(x,t), instead of exp(−ixt) in the unperturbed case. The perturbed kernel arises from first order eigenvalue problems with rank one perturbations.
Abstract LetBσ, p, 1⩽p⩽∞, be the set of all functions fromLp( ) which can be continued to entire functions of exponential type ⩽σ. The well known Whittaker–Kotelnikov–Shannon sampling theorem states that everyf∈Bσ, 2can be represented as[formula]in normL2( ). We prove that it is also true for allf∈Bσ, p, 1<p<∞, in normLp( ). From this, we further prove that iff(x)=O(Ψ(x)), whereΨ(x)∈Lp( ),Ψ(x)⩾0 is even and non-increasing on [0, ∞), andf(x) is Riemann integrable on every finite interval, then the aliasing error off, i.e.,f(x)−∑k∈ f(kπ/σ) sin σ(x−kπ/σ)[σ(x−kπ/σ)]−1, converges to zero inLp( ), 1<p<∞, whenσ→+∞. Iff∈Lrp( ),r∈ , we also determine the error bound of its aliasing error.
A multi-tenant virtual machine infrastructure (MTVMI) allows multiple tenants to independently access and use a plurality of virtual computing resources via the Internet. Within the MTVMI, different tenants may define unique configurations of virtual computing resources and unique rules to govern the use of the virtual computing resources. The MTVMI may be configured to provide valuable services for tenants and users associated with the tenants.
A multi-tenant virtual machine infrastructure (MTVMI) allows multiple tenants to independently access and use a plurality of virtual computing resources via the Internet. Within the MTVMI, different tenants may define unique configurations of virtual computing resources and unique rules to govern the use of the virtual computing resources. The MTVMI may be configured to provide valuable services for tenants and users associated with the tenants.
A multi-tenant virtual machine infrastructure (MTVMI) allows multiple tenants to independently access and use a plurality of virtual computing resources via the Internet. Within the MTVMI, different tenants may define unique configurations of virtual computing resources and unique rules to govern the use of the virtual computing resources. The MTVMI may be configured to provide valuable services for tenants and users associated with the tenants.
Existence of the density limit in the helicon plasma sources is revisited. The low-and high-frequency regimes of a helicon plasma source operation are distinguished. In the low-frequency regime with omega < root omega(ci)omega(ce), the density limit is deduced from the Golant-Stix criterion of the accessibility of the lower hybrid resonance. In the high-frequency case, omega > root omega(ci)omega(ce), an appropriate limit is given by the Shamrai-Taranov criterion. Both these criteria are closely related to the phenomenon of the coalescence of the helicon wave with the Trivelpiece-Gould mode. We draw a conclusion that the derived density limits are not currently achieved in existing devices, perhaps, because of high energy cost of gas ionization. (C) 2014 AIP Publishing LLC.
A differential microcalorimeter comprises a means for programmed heating of cells which accommodate heating and thermosensitive elements, a means for measuring power output of a thermal process under study, an a-c voltage source and a temperature measuring circuit, as well as a variable resistor for adjusting the baseline. The outputs of the means for measuring power output of a thermal process under study and of the means for programmed heating of the cells are connected, via appropriate phase-sensitive switches, to the second terminals of the series connected heating elements having their interconnected first terminals connected, via an appropriate phase-sensitive switch, to a movable terminal of the variable resistor for adjusting the baseline.
A machine provided with a bed on which is mounted a frame having an explosion chamber communicating with the space of a power cylinder whose plunger supports a punch, an anvil block located opposite to the punch and carrying a die arranged coaxially with the punch, and a device for returning the plunger to the initial position. The frame and the anvil block are rigidly secured on the bed, the space of the power cylinder is open at both ends and a hole providing communication between the space, the explosion chamber is located substantially in the middle of the length of the space, the plunger supporting the punch and a second similar plunger with a second punch being installed in the space opposite to the axis of the hole while a second anvil block is rigidly installed on the bed opposite the second punch symmetrically with the first anvil block relative to the same axis, the second anvil block being rigidly connected to the first anvil block and carrying a rigidly-secured second die. Due to the rigidity of its design, the machine ensures a higher working precision, efficiency and durability than other machines of the same type.
A differential scanning microcalorimeter comprising sample and reference calorimetric chambers. The chambers are made as elongated tubes and each is fitted with heater and temperature-sensing elements connected to a power measuring system of controlled thermal processes. In addition, each chamber is provided with an additional temperature-sensing element to separate its sensitive volume which is connected to a sensitive volume separation system. The output of the sensitive volume separation system is connected to an additional heater element placed on tubes external of the chamber sensitive volumes.