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Imaging of teeth is very important to doctors in the diagnosis and treatment of dental diseases. The main imaging modality currently used is Cone-Beam Computed Tomography (CBCT), which however suffers from ionizing radiation causing potential damage to human body. In this work, photoacoustic imaging is proposed for the imaging of tooth, specifically the tooth root. A photoacoustic digital phantom of the tooth is generated based on clinical CBCT data. The roots encased by alveolar bone are imaged by using the realistic photoacoustic digital phantom in the simulation study. Several image reconstruction algorithms are used and compared to remove the artifacts caused by heterogeneous acoustic velocity distribution.

The sampling noise cancellation (SNC) technique has been applied to different discrete-time circuits in recent literature, but the cost of this technique has not been well studied. This paper gives a detailed analysis of the SNC approach in a track-and-hold amplifier (THA). Closed-form expressions are derived for each noise source in the THA during the sampling phase and are verified by simulations. The analysis shows that while the sampling noise can be cancelled, the noise from the extra amplifier and switches can become dominant and even outweigh the benefits from SNC. Therefore, the SNC technique should be used with attention to the trade-offs, as described in this paper.

To further understand fermentation kinetics of sodium gluconate (SG) production by Aspergillus niger with different inlet oxygen concentrations, logistic model for cell growth and two-step models for SG production and glucose consumption were established. The results demonstrated that the maximum specific growth rate (µm) presented exponential relationship with inlet oxygen concentration and the maximum biomass (Xm) exhibited linear increase. In terms of SG production, two-step model with Luedeking-Piret equation during growth phase and oxygen-dependent equation during stationary phase could well fit the experimental data. Notably, high inlet oxygen concentration exponentially improved SG yield (YP/S), whereas biomass yield to glucose (YX/S) and cell maintenance coefficient (m) were almost independent on inlet oxygen concentration, indicating that high oxygen supply enhancing SG synthesis not only functioning as a substrate directly, but also regulating glucose metabolism towards SG formation. Finally, the applicability and predictability of the proposed models were further validated by additional experiments.

An understanding of nanocrystal shape evolution is significant for the design, synthesis, and applications of nanocrystals with surface-enhanced properties such as catalysis or plasmonics. Surface adsorbates that are selectively attached to certain facets may strongly affect the atomic pathways of nanocrystal shape development. However, it is a great challenge to directly observe such dynamic processes in situ with a high spatial resolution. Here, we report the anomalous shape evolution of Ag2O2 nanocrystals modulated by the surface adsorbates of Ag clusters during electron beam etching, which is revealed through in situ transmission electron microscopy (TEM). In contrast to the Ag2O2 nanocrystals without adsorbates, which display the near-equilibrium shape throughout the etching process, Ag2O2 nanocrystals with Ag surface adsorbates show distinct facet development during etching by electron beam irradiation. Three stages of shape changes are observed: a sphere-to-a cube transformation, side etching of a cuboid, and bottom etching underneath the surface adsorbates. We find that the Ag adsorbates modify the Ag2O2 nanocrystal surface configuration by selectively capping the junction between two neighboring facets. They prevent the edge atoms from being etched away and block the diffusion path of surface atoms. Our findings provide critical insights into the modulatory function of surface adsorbates on the shape control of nanocrystals.

Consider the statement:(1) What I am saying cannot be proved.Let us suppose that this statement can be proved. Then it must be true, i.e., in its own words, it cannot be proved, which contradicts our supposition.Therefore the statement cannot be proved, since our supposition has led to a contradiction. In other words, the statement is true. In this way we have proved the statement.Therefore the statement both can and cannot be proved.In the second part of the argument, if we speak of proving (1) in a given formal system S, then we cannot draw the conclusion that we have proved the statement in S. For it is possible that the argument cannot be formalized in S. Indeed, as we know, Gödel shows in his famous article of 1931 that for suitable systems S, it is possible to construct in S a statement saying in effect that the statement itself is not provable in S. The conclusion Gödel draws, we may recall, is that the statement thus constructed is true but not provable in S. Thus no contradictions arise in this way if we are confined to provability in a given system.A dual of (1) is the following:(2) What I am saying can be refuted.Let us suppose that this statement is true, or, in its own words, that it can be refuted. Then it must be false, which contradicts our supposition.Therefore the statement is false, since our supposition has led to a contradiction. In this way, we have refuted the statement. We see that the statement can be refuted; in other words, it is true.

A class A for which there is an infinite progression of classes A1, A2, … (not necessarily all distinct) such thatis said to be groundless. A class which is not groundless is said to be grounded. Let K be the class of all grounded classes.Let us assume that K is a groundless class. Then there is an infinite progression of classes A1, A2, … such thatSince A1 ϵ K, A1 is a grounded class; sinceA1 is also a groundless class. But this is impossible.Therefore K is a grounded class. Hence K ϵ K, and we haveTherefore K is also a groundless class.This paradox forms a sort of triplet with the paradox of the class of all non-circular classes and the paradox of the class of all classes which are not n-circular (n a given natural number). The last of the three includes as a special case the paradox of the class of all classes which are not members of themselves (n = 1).More exactly, a class A1 is circular if there exists some positive integer n and classes A2, A3, …, An such thatFor any given positive integer n, a class A1 is n-circular if there are classes A2, …, An, such thatQuite obviously, by arguments similar to the above, we get a paradox of the class of all non-circular classes and a paradox of the class of all classes which are not n-circular, for each positive integer n.