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It follows from the last three pairs of axioms above (identity, distributivity and complements), or from the absorption axiom, that

A Boolean algebra is a six-tuple consisting of a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary operation ¬ (called "complement" or "not") and two elements 0 and 1 (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols ⊥ and ⊤, respectively), such that for all elements a, b and c of A, the following axioms hold: 2

The relation ≤ defined by a ≤ b if these equivalent conditions hold, is a partial order with least element 0 and greatest element 1. The meet a ∧ b and the join a ∨ b of two elements coincide with their infimum and supremum, respectively, with respect to ≤.

The set of axioms is self-dual in the sense that if one exchanges ∨ with ∧ and 0 with 1 in an axiom, the result is again an axiom. Therefore, by applying this operation to a Boolean algebra (or Boolean lattice), one obtains another Boolean algebra with the same elements; it is called its dual. 3

do (1), (2), and (4) form a basis for Boolean algebra? Calling (1), (2), and (4) a Robbins algebra, the question then becomes: Is every Robbins algebra a Boolean algebra? This question (which came to be known as the Robbins conjecture) remained open for decades, and became a favorite question of Alfred Tarski and his students. In 1996, William McCune at Argonne National Laboratory, building on earlier work by Larry Wos, Steve Winker, and Bob Veroff, answered Robbins's question in the affirmative: Every Robbins algebra is a Boolean algebra. Crucial to McCune's proof was the automated reasoning program EQP he designed. For a simplification of McCune's proof, see Dahn (1998).

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Once the aircraft reached cruising altitude, the pilot came on the loudspeaker again…

Also, airline cockpit doors aren’t spring-loaded to snap shut when released. (Indeed, by FAA rules, when the plane is on the ground that door remains open. Passengers will recall that the cockpit door is open while they boarding and deplaning without anyone’s struggling to hold it open.) Fire axes, when they were carried, were often stowed within the cockpit itself, and most airlines still have a protocol in place holding that a flight attendant should step into the cockpit with the co-pilot if the pilot steps out (or vice-versa) so that no one is ever left alone on the flight deck. But all those safeguards were established back in the days when it was unanticipated that anyone (pilot or otherwise) would deliberately barricade himself inside a cockpit with the intent of crashing a plane.

Plattner continues: Suddenly, we hit a patch of turbulence. Nothing much, the cabin just shook a little for a moment. But the rubber band snapped off with a loud ‘ping!’ and went sailing down the aisle. The door promptly swung shut. A moment later, the pilot came out of the bathroom. When he saw the closed door, he stopped cold. I watched him from the back and wondered what was wrong. The stewardess came running up, and together they both tried to open the door. But it wouldn’t budge.

Jan 9th, 2017 An episode of the 1950s western TV series 'Trackdown' featured a character named Walter Trump who claimed he would build a wall in order to protect a town from the end of the world.

Among oscillators the new addition is the Triple Exponential Average. TRIX features a Triple Exponential Moving Average, and oscillates around a centerline at 0. Efficient filtering out of market noise is the greatest advantage of this indicator.

On the indicators front, we are most impressed by the TRIX and TEMA indicators. Both of them enable an incredible degree of clarity to potential trades, and make the evaluation of market action far more concrete and objective than what it was before. TRIX is a great oscillator that takes advantage of the clarity of TEMA to take us to the next generation of oscillators, in the process overcoming many of the traditional weaknesses of oscillators, namely lag, and susceptibility to whipsaws.. There is no question that the highlight of this new release is the powerful indicator pack which in itself justifies a move to a broker offering an MT5 trading experience.

Of these, the double exponential moving average (DEMA) is an advanced tool with lesser lag and greater accuracy than a simple EMA, and emits its signals by taking the n-period EMA of an EMA, hence the double MA name. Similarly a TEMA, or Triple Exponential Moving Average calculates the EMA of the n-period EMA of the raw price EMA, and is thought to suffer from even less lag than the double exponential moving average DEMA. All the moving averages are used in the manner that their more common simple and exponential moving averages are employed in trend analysis.

The total number of new indicators is seven. Among these, five new trend indicators clearly possess the greatest emphasis. The Double- and Triple Exponential Moving Averages, and their derivatives are the most exciting new additions to the MetaTrader toolbox, promising revolutionary changes to the way risk is analyzed and traded.

The greatest new additions are the large number of new indicators added to the already significant technical analysis collection of MetaTrader 4. Unlike in the previous version, MetaTrader 5 divides forex indicators into the four groups of “Trend”, “Oscillators”, “Volumes”, and “Bill Williams” indicators categories. A fifth category of custom indicators is also available where traders can store imported or developed items. The new indicator group system is suitable for the classification of the larger number of analytical tools – it makes access easier and faster.

The high-low method is subject to several problems that tend to yield inaccurate results. The problems are:

The high-low method is used to discern the fixed and variable portions of a cost. The concept is useful in the analysis of pricing and the derivation of budgets. It could be used to determine the fixed and variable components of the costs associated with a product, product line, machine, store, geographic sales region, subsidiary, or customer.

Because of the preceding issues, the high-low method does not yield overly precise results. Thus, you should first attempt to discern the fixed and variable components of a cost from more reliable source documents, such as supplier invoices, before resorting to the high-low method.

Example of the High-Low Method of Accounting

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Grant scammers generally follow a script: they congratulate you on your eligibility, then ask for your checking account information so they can “deposit your grant directly into your account,” or cover a one-time “processing fee.” The caller may even reassure you that you can get a refund if you’re not satisfied. In fact, you’ll never see the grant they promise; they will disappear with your money.

This article was previously available as Free Government Grants: Don't Take Them For Grant-ed.

The FTC says following a few basic rules can keep consumers from losing money to these “government grant” scams:

Some scam artists advertise “free grants” in the classifieds, inviting readers to call a toll-free number for more information. Others are more bold: they call you out of the blue. They lie about where they’re calling from, or they claim legitimacy using an official-sounding name like the “Federal Grants Administration.” They may ask you some basic questions to determine if you “qualify” to receive a grant. FTC attorneys say calls and come-ons for free money invariably are rip offs.

“Because you pay your income taxes on time, you have been awarded a free \$12,500 government grant! To get your grant, simply give us your checking account information, and we will direct-deposit the grant into your bank account!”

But the Federal Trade Commission (FTC), the nation’s consumer protection agency, says that “money for nothing” grant offers usually are scams, whether you see them in your local paper or a national magazine, or hear about them on the phone.